It might be a bit mental, but it'd be interesting to see a Christian Mohammed joining the Romans. Start off as an Orthodox philosopher, and spread the ideas of Islam as a philosophy rather than as a faith, or comes up with an equally compelling philosophy that supports Warrior-Priests and Arabian unification. That way he might still gain traction enough to gather some strength - and then start taking over central Arabia, with an envoy sent to Constantinople basically asking to be an ally/client - to get material aid as well as an agreement that Mohammed can keep Persian territories in Arabia unchallenged.
Having him basically form a federation of Rome-aligned client states would be interesting, and he could legit then retire from secular leadership to become the Metropolitan, or even Patriarch, of Mecca. (The latter might be hard to have recognised for a long time. Potentially after his death).
Actually, that could make the Great Mosque an interesting location. If the whole idea is that Mohammed goes out, and forces the groups he defeats to make him their leader, but doesn't dissolve them, instead making them join a conclave in the Great Mosque, he could set up a Federation where he leads every member (until he dies/resigns). (Side Note: Technically you can be governor of every US state, have fun with that TL). Set it up so that the Council of Tribes is presided over by the Metropolitan/Patriarch of Mecca, and you've got a Theocratic Republic in Mecca, both as ally of Rome, and well placed to dominate Middle Eastern and Indian Ocean politics.
Heck, you don't even need to change the TL that much, you could still have him and his Christians chased to Axum, who'll probably still be willing to assist a Christian Priest and his flock. You just need to have him convert to Christianity, and develop his philosophy.
(Side Note : Warrior Priests of Mecca sounds like an awesome group or an arabian heavy metal band. I'd prefer the warband.)
