I actually have a different question now: Islam certainly takes hold, but what if Khalid ibn Walid dies in one of those battles, and his army routed, buying time for the Romans and Sassanids? Or some other defeat?
There were Arab defeats at Roman hands in the early days so I'm tempted to say it may not make an awful lot of difference. Theophanes Confessor, for example, talks about Heraclius' brother Theodore routing an Arab army near Emesa and driving the Arabs away from Damascus.
Indeed, if Theophanes is to be believed, the whole fall of Syria may be understood in a similar way to the fall of Anatolia- Roman armies turning on each other to support a pretender to the throne and allowing the invaders in between them. Why this isn't discussed more I'm not quite sure. I didn't even notice that Theophanes mentions this until I re-read him last night. The joys of having Theophanes as a toilet book.
The quote in question (for the year AM 6126, which is late 634 and early 635AD) reads:
"Baanes' (a general chosen by Heraclius) men rebelled and chose him Emperor, renouncing Herakleios. Then the sakellarios' troops withdrew (the sakellarios in question is Theodore, a brother of Heraclius who had previously had success against the Arabs); the Saracens found an opportunity to join battle. Since the south wind was blowing against the Romans, they were unable to face their foes because of the dust, and they were defeated. They leaped into the Yarmouk river where it is narrow and were destroyed there."
Which is interesting to say the least. Theophanes' wider account has the Arabs capturing Damascus briefly the previous year and advancing deeper into Syria, where they are defeated by Theodore with significant loss of life. Arab reinforcements arrive and inflict a minor defeat on Theodore's troops, which causes Baanes' troops to panic and name their man Emperor. In the confusion, the Arabs are able to mop up these disorganised imperial armies, which may well have been attempting to retreat from Syria.
It's notable that Theophanes certainly had access to Arab and Syriac sources when writing his chronicle. Food for thought, anyway.