The arab invasion was preceded by the persian attack that devastated much of the empire including Syria and Egypt, that were later conquered by arabs, but also other regions were devastated in that war like Anatolia, the Balkans and even the islands of the Mediterranean and the Aegean seas, so the empire was much weaker then around 600 AD.
Before the war Arabia was divided between areas of influence of Rome and Persia so even the islamic unification of the arab peninsula was possible only because of the conflict that distracted romans and sassanids alike while destroying other arab entities like the christian Ghassanids, allies and subjects of the romans. Persian weakness was also a factor, a strong Persia would have probably hindered an arab attack on romans.
One advantage Arabs had was that their attack came from a surprising direction and romans had little defenses in southern Syria. Once Syria fell the main roman army had to defend Anatolia while the overland road to Egypt was cut and the small garrison there was left isolated. Another arab advantage was the religious fanaticism of their soldiers.
Without islam it is very likely that christianty would have eventually dominated Arabia.