Surely Khanid were integrated, and Udorians Reclaimed?
In any case, I'd assume that piety in itself doesn't matter (for a good enough actor, no one can know the "level of faith"). However, since church bureaucracy = Imperial bureaucracy, the person's position in the church is almost as important as his secular "caste". There's likely glass ceilings ("you have to be a noble to become a bishop") and so on, but I'd assume that serving the Faith well might be able to elevate a person into a higher caste. (Yes, even make one a Heir, if you happen to belong to high nobility and your house happens to be named "Ardishapur".)
Of course, this means that the Church is a battleground. A monastery is not a place where noble families send their black sheep to be out of eyes, out of mind. The smartest child might be prepared to take care of the family property, but the next-smartest is going to be either a soldier or a priest and an important piece in the Great Game the Holders play. There likely are a great number of religious orders, some of which may grant specific rights and privileges - for example, if your grand-grandson sits two rows ahead of the rival family's whelp in the service, holding that big candle, he might get to speak with higher-ranking people. Assuming he doesn't end up as their little plaything and dead, might secure your family a mighty patron (and some money). Or possibly both, where the family gets some favours from the Holder for whom the kid with the bad luck died for.