Yes but how would that conversion start? Why would it catch on in the far off west? Why would anyone send missionaries there? Why would Zoroastrians make a concerted effort at evangelism when they had by that point pretty thoroughly adopted a viewpoint of philosophical tolerance towards other faiths?
The movements of people are the best missionaries (I'm not even sure Zoroastrians
had missionaries), so you really only need a group of Zoroastrians to move there and gain prominence. It could be slowly, only fully kicking in after Rome is starting to fall apart and then become somewhat all encompassing in the west or it could gain it almost immediately. Say, a general from the east is a Zoroastrian, in order to limit his influence but not outright kill him because of his connections to Rome itself, they "send him to Mongolia" with most of his immediate followers. Once the man becomes a threat, someone kills him. His followers, however, remain and the faith spreads through the area.