I would imagine it depends on where exactly they end up. France and Spain would be quite hostile to Zoroastrians, I imagine, as certain aspects of that religion reek of the recently-crushed Catharist heresy. Other countries might be more tolerant--Poland-Lithuania in particular, as the prevailing ideology at that state's height held that the Polish aristocracy are more closely related to eastern steppe peoples like Persians and Turks than to anyone else, and some religious toleration was extended to those believed to share this ancestry (like the Lipka Tatars).
Though perhaps their presence would accelerate the development of Indo-European language theory, and maybe inspire some Pan-IE sentiment among the cultured classes.
Economics would also have a part to play in how they are received--the need to populate the more sparse parts of Europe east of the Elbe would create an incentive for toleration that is absent in France.
As to Zoroastrianism's relationship with Christianity, I'd say it's more like an uncle-by-marriage than a parent--Christian theology and philosophy also draws heavily on Hellenic sources, which I think play a greater role than do Zoroastrian teachings.
Interesting - I agree that the best case scenario for a Zoroastrian community that decides to settle in medieval or premodern Europe would be to follow the fate of the Tatar communities in Poland, Lithuania, Belarus, and Finland.
I don't necessarilly agree that a Zoroastrian presence in medieval or premodern Europe would speed up development of Indo-European linguistic study, however, as the Roma people were also an Indo-Iranian-speaking community who originated far beyond Europe who lived there for many centuries.
I suppose it also depends on when the Zoroastrians enter Europe - The Parsis arrived in India over one thousand years ago, while the Iranis only migrated there in the last few centuries.