Quite simply, no. Not to any meaningful extent. Even mentions in classical sources are few and far between.

It's important to understand that while Zoroastrianism, unlike many other ancient belief systems, had doctrinal and confessional elements, ritual practice was still its core. While the fire temples and their elemental ritual purity would have constituted a significant difficulty to replicate outside established communities, those material aspects wouldn't have been insurmountable. Probably the biggest obstacle would instead have been the necessity of reciting sacred hymns, a duty that until the 4th century was passed on orally within the priesthood (particularly associated with a Median tribe, the Magoi). Losing the opportunity of maintaining ritual purity (and thus protection in spiritual warfare) and being surrounded by nonbelievers who didn't even care to do so, would surely have been a deeply unattractive prospect to a devout Mazda-worshipper.

We're talking about a practice within a complex social organization in a deeply tribal society, moreover a system of belief which was by that time connected to the royal ideology established by Darius the Great and thus hardly separable from the Iranian empires themselves. Before the destruction of Sasanian dominion, it seems like the social conditions under which an exodus of large enough groups of Mazda-worshippers might have occurred just didn't arise. I think one could make geographical arguments to bolster this, but I'd be going too far to do that here - but you do find a bit more movement across the Central Asian steppes than in the West, for natural reasons.