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It wouldn't be the official religion of the state, but the emperors and city dwellers wouldn't magically become pagan again. I think actually there would be alot more Arians and other Christian heresies, since the edict was was used to promote Nicene Christianity
It's depends really on what route this Muhammad guy would take, doesn't it? If he went for peaceful, well we already have Christianity for that. If he goes for conquest though, I could see him take off for a bit, till the inevitable overreach and him getting smacked down by the governor of Egypt...
and those are just less known donatists. Seeing as Cathar comes from greek "the Pure" could it just be a offhand for heretics who considered themselves more pure then accepted christianity (or am I reading too much into that)?