Democracy wopuld be delayed, but i doubt the new persian backed regiem would last long once persian attention looked elswhere.Once the persian empire collapsed, Athens, now with persian as well as greek way of thinking and more determaind then ever not to be enslaved and too protect its empire takes advantage of the chaos and starts an empire-with no macadon or a more powerful sparta opposing them. ( so yes-a big pod-but not in the way you might expect and certainly overplayed.)
Why no Macedon?
Iirc the King of Macedon was a Persian vassal at this time, and would likely have become their "Satrap" in Hellas post victory. As Persia declines, he likely becomes more independent, so perhaps we get "Alexandr" a century earlier.