I think most arabs would become Christians or Jews.
That's one of the more likely possebilities, allthough Manicheism and several other religious movements also had quite a few adherants among the Arabs.
My guess is that, for at least the first three or four centuries, Arabia would remain religiously diverse, with significant numbers of pagans, Jews, and Nestorian and Syriac Orthodox Christians, while Manicheism and various Gnostic, Christian and other sects would also have smaller but still significant numbers of adherants.
The influence of the large Christian denominations would gradually become stronger as the Christian Arab tribes and kingdoms in the north and the Axumites in the south become stronger and expand their influence deeper into the Peninsula.
Also I don't see the Byzantines being able to hold on to the Levant and Egypt for all eternity. The religous schism between Constantinople and the Eastern Churches had made most people very unsatisfied with Byzantine rule.
Egypt could indeed be lost, especially during the period right after the war of 590-630.
However, I can see the Byzantines holding on to the Levant for quite a while; Syria was still not as heavily populated as Egypt was, and you have to keep in mind that there were a lot of Greeks and Melkites in the Levant as well.
And if Egypt is lost as a result of a major Coptic rebellion, then many Egyptian Melkites would end up fleeing to Byzantium, and odds are that many of them would end up in the Levant. In OTL, many Egyptian Melkites fled to the Exarchate of Africa after the Muslim invasion, but as long as Byzantium holds on to the Levant ITTL (which is a rather likely thing to happen), many of these refugees will end up in the Levant instead.
The Arabs were IRL even seen as liberators, since they allowed much more religious freedom than the Emperor in Constantinople.
The general attidute of the Miaphysite and Nestorian Christians towards the Muslims right after the conquest usually varied between indifference and mild enthusiasm.
Yes, I'm aware of the various Medieval Egyptian and Syrian Christian writers who graphically described the atrocities and repression that their people suffered under Byzantine rule, and how the Arabs liberated them.
And though I do not deny the fact that the Miaphysites and Nestorians indeed did suffer under Byzantine rule, I do hold
some reservation towards such claims, as said writers could very well have had political reasons aside from purely historiographical reasons for portraying the Byzantines and the Muslims the way they did.
One has to keep in mind that these writers were living under Muslim rule, and as the Byzantines were still enemies of the Muslims and as some Muslim rulers indeed did suspect their Christian subjects of sympathizing with the Byzantines, one can imagine that those writers had several good reasons to portray the Muslims as liberators while denouncing the Byzantines and emphasise the oppression they suffered under them.