A successful Persian subjugation of Greece might have resulted in a calm and orderly region, thus making it unnecessary for Rome to keep the peace (which was why Rome took over Greece in the first place). However I don’t see that as being likely. More likely, the unruly Greeks would have been trouble for Persian satraps. After Rome’s defeat of Carthage, they would have learned to pit Roman interests against Persian interests or outright appealed to Rome for aid. This would have resulted in war between Rome and Persia over Greece. The Persian army would have been no match for the legions, and Rome’s fleet would control the sea.
good analysis. Though the Persian army did hold the Byzantines for centuries.