Short answer
No. The Gospels show Jesus praying by falling on his face to the ground, by kneeling, and alone in secret. They never show him praying with musical instruments, or leading worship with music. Once, after the Passover meal, he and his disciples sang a hymn before they went out. But his prayer itself was bowing low before God (﷾). The early Church objected to instrumental music in worship. A Catholic encyclopedia of 1911 says strong objection to the organ in church services lasted until about the twelfth century. Muslims pray as the Gospels show Jesus praying: standing, bowing and putting the face to the ground. The Qur'an is recited in prayer, never played with instruments.
Full explanation
How Jesus prayed
In Gethsemane, Matthew says, Jesus "fell on his face, and prayed". Mark says he fell on the ground and prayed. Luke says he kneeled down and prayed. He taught his disciples to pray in secret, with the door shut, not to be seen by others, and not to use vain repetitions. None of the Gospels shows him praying with instruments, or with a band, a choir or an organ.
“And he went a little further, and fell on his face, and prayed, saying, O my Father, if it be possible, let this cup pass from me: nevertheless not as I will, but as thou wilt.”
“And he went forward a little, and fell on the ground, and prayed that, if it were possible, the hour might pass from him.”
“And he was withdrawn from them about a stone’s cast, and kneeled down, and prayed,”
“And when thou prayest, thou shalt not be as the hypocrites are: for they love to pray standing in the synagogues and in the corners of the streets, that they may be seen of men. Verily I say unto you, They have their reward. But thou, when thou prayest, enter into thy closet, and when thou hast shut thy door, pray to thy Father which is in secret; and thy Father which seeth in secret shall reward thee openly. But when ye pray, use not vain repetitions, as the heathen do: for they think that they shall be heard for their much speaking.”
The one hymn
Matthew does record that after the Passover meal, Jesus and his disciples "sung an hymn" and went out to the Mount of Olives. Singing praise to God (﷾) is not forbidden. But this was a hymn at the end of a meal, not the way he prayed. When he prayed, he bowed to the ground.
“And when they had sung an hymn, they went out into the mount of Olives.”
“And he went a little further, and fell on his face, and prayed, saying, O my Father, if it be possible, let this cup pass from me: nevertheless not as I will, but as thou wilt.”
Instruments came into church worship later
The Catholic Encyclopedia of 1911 says that in the early centuries the Church objected to instrumental music in worship. The objection applied to the organ too, which people linked with the theatre and the circus. A late report says Pope Vitalian brought the organ into church in the seventh century. But the encyclopedia calls this very doubtful. It says strong objection to the organ in church services stayed fairly general until the twelfth century. Only after that did the organ become the church's favoured instrument.
In its section on the organ in church service, says that in the early centuries the Church objected to instrumental music, and that this objection applied also to the organ, which was linked with the theatre and the circus. It calls doubtful the late report that Pope Vitalian (657-672) brought the organ into church services, and says a strong objection to the organ in church service remained fairly general down to the twelfth century, after which it became the favoured church instrument.
Why many churches use music
Many Christians point to the Psalms, which call for praising God (﷾) with trumpet, harp, stringed instruments, organs and cymbals. They also point to Paul. He tells believers to speak to one another in psalms, hymns and spiritual songs, "singing and making melody in your heart to the Lord".
“Praise him with the sound of the trumpet: praise him with the psaltery and harp. Praise him with the timbrel and dance: praise him with stringed instruments and organs. Praise him upon the loud cymbals: praise him upon the high sounding cymbals.”
“Speaking to yourselves in psalms and hymns and spiritual songs, singing and making melody in your heart to the Lord;”
Prayer as the prophets prayed
The Qur'an tells believers to bow down, prostrate themselves and worship their Lord. In Muslim prayer the worshipper stands, bows and puts his face to the ground, as the Gospels show Jesus doing in Gethsemane. The Qur'an is recited aloud in the prayer, with care and beauty, but no instrument is played. The prayer of a Muslim looks more like the prayer of Jesus than the worship of most churches does.
“O ye who believe! bow down, prostrate yourselves, and adore your Lord; and do good; that ye may prosper.”
“And he went a little further, and fell on his face, and prayed, saying, O my Father, if it be possible, let this cup pass from me: nevertheless not as I will, but as thou wilt.”
Perspectives
Christian
Many Christians say music and singing are a fitting way to worship God, as the Psalms and Paul teach.
The Psalms call for praising God with trumpets, harps and other instruments.
Rebuttal
The Psalms belonged to the worship of the Temple, which also offered animal sacrifices that churches no longer keep. The early Church itself objected to instruments in worship. And Jesus' own prayer was falling on his face before God (﷾).
Paul tells Christians to sing psalms, hymns and spiritual songs.
Rebuttal
Paul speaks of "making melody in your heart" and names no instrument. These are Paul's words, while the Gospels show Jesus praying by kneeling and falling on his face.
The Islamic perspective
The Gospels show Jesus praying by bowing to the ground, not with music. The early Church objected to instruments in worship. Muslims pray as he did, standing, bowing and prostrating, and recite the Qur'an without instruments.
The Gospels show Jesus praying by falling on his face and kneeling.
The Catholic Encyclopedia says strong objection to the organ in church services lasted until the twelfth century.
The Qur'an tells believers to bow down and prostrate themselves in worship.