There were going to be Arabic invasions, with or without Islam. There was already an extensive migration of Arabs into parts of modern day Syria, Jordan and Iraq long before Mohammed came along. They'll be likely be a lot more disorganized and be akin to the Germanic invasions of western Europe, or not.
I'm not sure about that. There was, I believe, raiding into Roman Syria-Palestine, particularly after Maurice wound up the Ghassanids, but there had always been raiding, and it'd done very little damage to the surrounding area. I'm not an expert, but I'd be pretty surprised if non-Islamic Arab invasions were as dangerous as the Germanic invasions were. Even fourth century Germania looks like a verdent garden of Eden with a booming population compared to seventh century Arabia.
I think that if one is to draw comparisons to Germanic attacks, it's probably better to compare these theoretical pagan Arab attacks to those of the Germans in the second and third centuries- occasional, violent attacks that do a large amount of damage, but ultimately make very little difference to the broader strategic balance.
As for the survival of Hellenism, one can do it by preventing the Arab conquest of the Roman East, but one can do it equally well by having the Romans go under as OTL, and having the Sasanians survive. A Caliphate focused on Syria, Egypt and Palestine, but without Persian influence, is going to be a Caliphate that will inevitably follow Graeco-Roman, Mediterranean cultural norms, rather than Iranian ones. Basically, see what the Ummayads were doing, and then extend that.