That depends on exactly what Mohammed does when and after he becomes Christian.
For example, if he becomes a Melkite (= adhering the official imperial Church), then the Byzantine government will leave him alone, and the Byzantines might even support him to spread the teachings and influence of the official Byzantine Church among the Arabs, both among Arabs in Byzantine Syria and Palestine (where the "heretical" Syriac Orthodox Church was popular among Arabs) as well as among Arabs in the Hijaz and maybe even the other parts of the Peninsula as well.
However, if he joins the Syriac Orthodox Church (a.k.a. Jacobite) or the Church of the East (a.k.a. Nestorian), then things would take quite a different turn.
The adherants of both of these Churches were repressed in the Byzantine Empire as well as the Persian Empire, and both Churches had significant numbers of Arabian adherants, including powerful Arabian aristocrats (The Ghassanids were Syriac Orthodox and ruled Syria on behalf of the Byzantines, and the Lakhmids were Nestorians and ruled southern Mesopotamia and parts of the northern Peninsula and were vassals of the Persians, until those same Persians destroyed their kingdom somewhere around 600 AD).
And several Ghassanid as well as Lakhmid kings had the desire to conquer and control the entire Arabian Peninsula and unite all Arabs under their rule. If Mohammed became either a Jacobite or Nestorian Christian, then, given what he did in OTL, it is not at all unlikely that he will unite the Arabs and inspire them to overthrow the Persians and Byzantines that oppress them and conquer the pagan parts of the Arabian Peninsula for 'the One True Faith'.
In that scenario, it would be interesting to see what he does next - will he preach Arab chauvinism and brotherhood, or will he extrapolate this "standing up for the oppressed" to the many non-Arab followers that his Church has?
If he would have become Nestorian, then this would give him a good reason to call his followers to liberate the oppressed Nestorians in the Persian Empire. And in the case he became a Jacobite, he'd propably do the same, but then with the Byzantine Empire.
...and then it would also be very interesting to see how he will treat the Arab Christians that follow a different Church and teachings; will he acknowledge these other Christians as real Christians, or will he reject their faith to the extent that he defines them as heretics or infidels?
Or will he just reject some of their teachings, and say "you have your faith, and I have mine"?
Or will he just say that in the end, no human being knows the Truth, and that that makes all our beliefs so flawed that none can claim that his teachings and dogma's are superior to those of all others?
..
And then there is of course also the possebility that he goes his own way, and establishes a new sect or Church alltogether.
That would propably result in some Church of Arabia, or if he is less successful, a Christian community that's not unlike the Maronites.
What this Church will look like depends on what traditions and teachings will influence Mohammed's teachings.
The Byzantine Empire had exiled many small heretical sects to Mesopotamia and Arabia, and because of that, there were several small Christian and pseudo-Christian sects in the Hijaz at the time. And all of these sects could affect Mohammed and his teachings in some way.
And then, according to some 6th century Christian writers (IIRC), there was also an Arab monotheistic sect somewhere in the Hijaz that had adopted much of the religious laws of the Jews, and sought to follow the religion of Abraham.
If this sect indeed existed (which is not unlikely), then it is also quite likely that a Christian Mohammed would adopt some of their teachings, and maybe even absorbs the movement at some point.
...and in that scenario, you'd propably get some kind of "Islamochristianity" that is quite different from the other branches of Christianity. This type of Christianity would most propably focus on Ishmael as an important character, and the things that God had promised his descendants, and it would propably observe many of the Mosaic laws as well, although this would not make them unique among Christians, as the Coptic and Ethiopian Christians also observe many of these laws.