For certain time periods, yes. Which is reflected in EB's Parthian roster.
You got it the wrong way around. The Persians were bowmen (including HAs) right from the start - even in Achaemenid times.The more exposure the Persians had with Scythians and steppe cultures it seems they adopted the bow more often.
Unless of course you mean the specific Arsacid and Sassanid dynasties. They just adjusted their tactics and armaments to whatever enemy they had to fight. Sometimes that means reverting to neglected traditions...
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