Actually no, not easily. I think Aurvandil would have to declare war on their realms first to even arrest them. At that point, the priests could be tortured (for no lasting effect since it has no impact on the skills that matter to priests), but not banned or executed unless they had been caught doing something criminal. Basically only actions that could cause a priest to be arrested upon a failure (like an RTO) would subject the priest to a ban or execution if they got caught in the act.
Which produces all sorts of lulzy possibilities if major religions decided to get serious about taking down Aurvandil.
