Short answer
No. The Qur'an calls Satan the open enemy of mankind, and everything it teaches works against him. It forbids worshipping anything but God (﷾), the sin Satan most wants. It tells its readers not to follow his footsteps, and to seek refuge in Allah (﷾) from him before they recite. It says no evil ones brought it down: it would not suit them, nor could they. Jesus gave the same answer when he was accused of casting out devils by the prince of devils. If Satan cast out Satan, he said, his kingdom could not stand. The Prophet's (ﷺ) companions saw the angel Gabriel come, in the form of a man, to teach them their religion. A message that turns people from Satan to God (﷾) alone is not Satan's work.
Full explanation
What Satan would want, and what the Qur'an teaches
Satan's aim, in the Bible and the Qur'an alike, is to turn people away from God (﷾). The Qur'an does the opposite at every turn. It calls Satan an enemy and tells its readers to treat him as one. It says God (﷾) told the children of Adam not to worship Satan. It warns them not to follow his footsteps, since he commands what is shameful and wrong. It tells them to seek refuge in Allah (﷾) from Satan before they recite the Qur'an itself. Its last chapter is a prayer for protection from the whisperer who hides. A book written by Satan would be a book against himself.
“Verily Satan is an enemy to you: so treat him as an enemy. He only invites his adherents, that they may become Companions of the Blazing Fire.”
“"Did I not enjoin on you, O ye Children of Adam, that ye should not worship Satan; for that he was to you an enemy avowed?-”
“O ye who believe! follow not Satan's footsteps: if any will follow the footsteps of Satan, he will (but) command what is shameful and wrong: and were it not for the grace and mercy of Allah on you, not one of you would ever have been pure: but Allah doth purify whom He pleases: and Allah is One Who hears and knows (all things).”
“When thou dost read the Qur'an, seek Allah's protection from Satan the rejected one.”
“Say: I seek refuge with the Lord and Cherisher of Mankind, The King (or Ruler) of Mankind, The god (or judge) of Mankind,- From the mischief of the Whisperer (of Evil), who withdraws (after his whisper),- (The same) who whispers into the hearts of Mankind,- Among Jinns and among men.”
Jesus gave the same answer
When Jesus cast out devils, the Pharisees said he did it by Beelzebub, the prince of the devils. Jesus answered that every kingdom divided against itself is brought to ruin. If Satan cast out Satan, he said, he is divided against himself, so how could his kingdom stand? The Qur'an casts Satan out at every turn: it forbids idols, calls people to worship God (﷾) alone, and names Satan as their enemy. A Christian who accepts Jesus' answer has the answer to this charge too.
“But when the Pharisees heard it, they said, This fellow doth not cast out devils, but by Beelzebub the prince of the devils. And Jesus knew their thoughts, and said unto them, Every kingdom divided against itself is brought to desolation; and every city or house divided against itself shall not stand: And if Satan cast out Satan, he is divided against himself; how shall then his kingdom stand?”
“But if I cast out devils by the Spirit of God, then the kingdom of God is come unto you.”
Known by its fruits
Jesus said false prophets are known by their fruits. The fruit of the Qur'an in seventh-century Arabia was the end of idol worship, of burying baby girls alive and of drinking and gambling, and the start of daily prayer, fasting and charity to the poor. It brought people to honour Jesus and Mary and to worship the God (﷾) of Abraham alone. These are not the fruits Jesus said would mark a false prophet.
“Beware of false prophets, which come to you in sheep’s clothing, but inwardly they are ravening wolves. Ye shall know them by their fruits. Do men gather grapes of thorns, or figs of thistles? Even so every good tree bringeth forth good fruit; but a corrupt tree bringeth forth evil fruit. A good tree cannot bring forth evil fruit, neither can a corrupt tree bring forth good fruit. Every tree that bringeth not forth good fruit is hewn down, and cast into the fire. Wherefore by their fruits ye shall know them.”
“When the female (infant), buried alive, is questioned - For what crime she was killed;”
“O ye who believe! Intoxicants and gambling, (dedication of) stones, and (divination by) arrows, are an abomination,- of Satan's handwork: eschew such (abomination), that ye may prosper.”
“He said: "I am indeed a servant of Allah: He hath given me revelation and made me a prophet;”
“Behold! the angels said: "O Mary! Allah hath chosen thee and purified thee- chosen thee above the women of all nations.”
What the Qur'an says about evil spirits
The Qur'an answers the charge itself. It says no evil ones brought it down: it would neither suit them nor would they be able, and they have been kept far even from hearing it. The angel who brought it was seen. In a well-known report, a stranger in very white clothes, with no sign of travel on him, sat before the Prophet (ﷺ) and asked him about Islam, faith and excellence in worship. Afterwards the Prophet (ﷺ) told Umar that it was Gabriel, who had come to teach them their religion.
“No evil ones have brought down this (Revelation): It would neither suit them nor would they be able (to produce it). Indeed they have been removed far from even (a chance of) hearing it.”
Umar ibn al-Khattab reports that a stranger in very white clothes came and questioned the Prophet (ﷺ) about Islam, faith and excellence in worship, and then about the Hour. The Prophet said the one asked knew no more than the one asking, and gave two of its signs: a slave woman will give birth to her mistress, and you will see barefoot, poorly clothed, destitute shepherds competing with one another in raising tall buildings. Afterwards the Prophet told Umar the stranger was the angel Gabriel, who had come to teach them their religion.
The replies answered
Qur'an 22:52 — Surat al-Hajj (The Pilgrimage), verse 52
“Never did We send a messenger or a prophet before thee, but, when he framed a desire, Satan threw some (vanity) into his desire: but Allah will cancel anything (vain) that Satan throws in, and Allah will confirm (and establish) His Signs: for Allah is full of Knowledge and Wisdom:”
Cited for
The Qur'an itself admits that Satan threw words into what prophets recited. That verse was revealed because of the Satanic verses.
The response
The verse says the opposite of what the charge needs. It says Allah (﷾) cancels whatever Satan throws in and confirms His own signs. On the critics' own telling, the words were removed and the surah went on to call the goddesses nothing but names. That is the Qur'an defeating Satan, not Satan writing the Qur'an. And the story itself has no sound chain: Ibn Kathir found every version broken.
Where it lands — Even the verse critics cite says God (﷾) cancels Satan's words and keeps His own.
Ahmed, Before Orthodoxy (2017)
A study of the reports of the "Satanic verses" incident. Ahmed argues that many Muslim historians and commentators of the first two centuries passed the story on without finding it a problem, and that later Muslim scholarship came to reject it.
Cited for
A Harvard scholar showed that early Muslims themselves believed the Satanic verses story.
The response
Shahab Ahmed showed that many early historians passed the story on, and that later scholars rejected it. The hadith critics' reason was the chains: as Ibn Kathir noted, none reaches an eyewitness soundly. The sound report of the scene, in al-Bukhari, has no praise of idols. A report is weighed by its chain, not by how often it was copied.
Where it lands — The story was passed on by some early historians but has no sound chain, and the sound report of the scene does not contain it.
Sahih al-Bukhari 4862 — Kitab al-Tafsir (Prophetic Commentary on the Qur'an), hadith 4862
Ibn Abbas reports that the Prophet (ﷺ) prostrated when he finished reciting Surat al-Najm, and all the Muslims and the pagans, jinn and men, prostrated with him.
Cited for
Al-Bukhari says the pagans prostrated too. Why would they, unless their gods had just been praised?
The response
The report gives no reason, and it does not say their gods were praised. The surah ends with a command to fall down in prostration to Allah (﷾). The same surah, recited to them, calls their goddesses nothing but names. Whatever moved them that day, the words they heard condemned their idols.
Where it lands — The sound report records the prostration, not any praise of the idols.
Deuteronomy 18:20 — Torah, Devarim, chapter 18, verse 20
“But the prophet, which shall presume to speak a word in my name, which I have not commanded him to speak, or that shall speak in the name of other gods, even that prophet shall die.”
Cited for
By this story the Prophet (ﷺ) fails the Bible's own test: a prophet who speaks in the name of other gods must die (Deuteronomy 18:20).
The response
The charge stands or falls with the story, and the story has no sound chain. The Prophet (ﷺ) spent his whole mission calling people away from those very idols to Allah (﷾) alone. The surah in question calls the goddesses nothing but names, and it opens by saying he does not speak from his own desire. Al-Razi pointed out that praise of the idols later in the same surah would have proved those words, and the Qur'an, false on the spot. Nothing in the Qur'an speaks in the name of another god.
Where it lands — He never spoke in the name of other gods: the charge rests on a story with no sound chain.
Ibn Kathir, Tafsir, on Qur'an 22:52
Ibn Kathir notes that many commentators tell, at this verse, the story of the cranes (al-gharaniq), the praise of the idols said to have been spoken during Surat al-Najm. He says these reports all come through mursal chains, broken before they reach an eyewitness, and that he does not think any of them may be regarded as sound.
Cited for
No Muslim would invent a story that embarrasses the Prophet (ﷺ). So it must be true.
The response
Embarrassment is only a rough guide for historians: it cannot make a report true when its chain fails. Muslim scholars knew that some people invented reports, so they weighed every report by its chain, and this one has no sound chain. And to those who told it, the story did not end in shame. It ended with Allah (﷾) cancelling Satan's words and guarding His Prophet (ﷺ) (22:52). Later scholars rejected it, and al-Razi called it false and invented, against the Qur'an, the Sunnah and reason.
Where it lands — A story is not true because it is awkward; this one fails on its chains.
Corpus Coranicum
A long-term research project that publishes photographs and descriptions of early Qur'an manuscripts from libraries around the world, with radiocarbon results where they exist, so that anyone can compare them with the printed text verse by verse.
Cited for
The Satanic verses were once part of the Qur'an and were later taken out.
The response
No copy of the Qur'an, early or late, has them. Even the story has them taken back, never kept as revelation. Their key word, gharaniq (cranes), appears nowhere in the Qur'an. And praise of the idols runs against the whole surah: three verses later it calls them nothing but names that the pagans and their fathers made up.
Where it lands — No manuscript of the Qur'an contains the words.
Perspectives
A spirit not from God
Some Christian writers say the spirit that spoke to Muhammad (ﷺ) was not from God. They say it was a deceiving spirit, because the Qur'an denies that Jesus is the Son of God.
John's first letter gives a test of spirits. A spirit that does not confess that Jesus Christ is come in the flesh, it says, is not of God. It is the spirit of antichrist. The Qur'an denies that Jesus is the Son of God, so it fails this test.
Rebuttal
The test John gives is whether a spirit confesses that Jesus Christ is come in the flesh. The Qur'an calls him the Christ, the Messiah, born of Mary, and says he and his mother ate their daily food. By the words of the test, the Qur'an confesses it.
Early Muslim histories tell a story that Satan once slipped words into the Prophet's (ﷺ) recitation. The words praised the pagan goddesses, and they are called the Satanic verses.
Rebuttal
Every chain of that story is broken before it reaches an eyewitness, as Ibn Kathir noted, and hadith critics rejected it. The sound report of that scene has everyone prostrating at the end of Surat al-Najm, with no praise of idols. And the surah calls those goddesses nothing but names.
The Islamic perspective
The Qur'an came from God (﷾) through the angel Gabriel. It names Satan the enemy of mankind and turns people from him to the worship of God (﷾) alone, which is the opposite of Satan's work.
The Qur'an calls Satan an enemy, to be treated as one.
The Qur'an tells its readers to seek refuge in Allah (﷾) from Satan before reciting it.
The Qur'an says no evil ones brought it down, and that they could not.
Jesus answered that a Satan who cast out Satan would be divided against himself.
The Qur'an was brought by the angel Gabriel from God (﷾).