Were ancient Greeks and Persians aware of their Indo-European roots?

Vote #1 Daniel Ross: Daniel Ross’ answer to Were ancient Greeks and Persians aware of their Indo-European roots?

I don’t have a rabbit to pull out of my hat, like Daniel Ross mentioned I did for Latin and Greek. But there is a related question:

History: During Alexander’s invasions, would his soldiers have found Old Persian or Indic to be somewhat familiar sounding given their closeness to Greek?

And my take in that question was:

Probably. And they probably wouldn’t have cared.

Not aware of any ancient authority explicit pointing out cognates, even though some words of Old Persian Herodotus cited were, I think, cognates.