Well, in one of my games I had the red court infiltrate an entire church, so I guess anything is possible. If there's a good reason the character would be enthralled without his faith interfering with the enthrallment, that's perfectly legit.
I would think that maybe you'd need something more than just a powerful black court vampire to enthrall, or a true believer's faith would shield him from that. But how about a personal vector that would allow the black court to sort of circumvent that? Turn a family member and train him to enthrall the true believer. The personal connection and the blood relation should be enough to bypass any protection the faith may present, and you've got yourself not only a fine thrall, but also a cool story around that.
When it comes to using the faith powers, you could have it hint at his enthrallment, but not break it. Maybe he gets a headache when doing too much with them, leading him to believe he's got the flu or something.