The Ghassanid and Lahkmid rivalry is still in place, so the relationship between Arab mercenaries and the northern Empire is still there. I see no reason for the change in Roman politics to delay the Aksumite invasion of Himyar, which is one of the major events leading to Mohammed. So yeh, there seems to be no necessary reason to change the basic trajectory of the Muslims

Now, if Aaron wants to RP a historical Caliph or make up his own, that is his choice.