I don't think it makes much difference.
The history leading up is that Justinian was bent on reconquering much of the Western Roman Empire. And he did pretty good, nailing down Yugoslavia, Italy, Spain and north Africa.
However, the Persians were a constant threat. So Justinian, as did previous Roman and Byzantine rulers, bought the peace with gifts. Basically: They paid tribute.
The Romans and Persians had been traditional enemies all over the middle east. At times, the Romans had pushed as far Mespotamia, but the Persians had pushed them back out. There were no real natural borders of demarcation, so Assyria and Palestine were simply notional places.
Anyway, Justinian's successors, as I recall, just decided to stop paying tribute. All those conquests were expensive, costs had to be cut somewhere.
The Persians invaded, sweeping the Arabian peninsula, driving into Syria and Palestine, taking Egypt and even pushing into Anatolia. Eventually, the Byzantines pushed them back out, and something resembling a status quo was restored.
But the trouble was, neither could really overcome the other decisively. Instead, they had bankrupted their treasuries, wrecked their armies and done considerable damage to their subject peoples.
It was in this state of complete exhaustion of the superpowers that Islam took place.
Mohammed united the Arab peoples of the Arabian peninsula for the first time. These included everything from settled and civilized traders and urbanites in Yemen, Mecca and Medina, to barbarian tribesmen in the hinterlands.
They came boiling out, and neither the Byzantines nor the Persians had the strength to stop them. In short order, Assyria, Palestine and then Egypt and Libya fell. Mesopotamia and Persia collapsed. The Byzantines barely threw them back from Anatolia.
If we assume that the whole Roman Empire was still around, I don't think it makes much of a difference. Had the whole of the Roman Empire went up against the Persians, I think the ultimate outcome remains. The Romans could not take the Persians down. At most, the Romans might have been able to prevent the wave of Persian conquests. But the end result would be the same, bankrupt treasuries and exhausted armies.
The Romans had no way to control the Islamic movement. At best, they would have seen it diverted into Mesopotamia and Persia. But then, the new Caliphate turns around and attacks with Arabia, Mesopotamia and Persia. The Romans could barely handle Persia alone.
There's no geographical barriers protecting Assyria or Palestine, and Egypt is sitting there like a plum. Sooner or later these would have fallen, and likely more sooner than later.
After that? Maybe Carthage and Algeria would have held out. That's iffy. Most likely, the Romans would have stopped the Caliphate at Morocco, no Spanish adventure. No conquest of Sicily. But that's it.