Yes, Frau would have been pretty furious with Teito for revealing all of that. Unfortunately, considering Zehel's symbol was so visible on his chest the fact that he was a ghost would have been revealed anyways. It wasn't like Teito knew what Frau usually told people either, so he couldn't really be blamed.

Not that Frau would know at the moment. He was far too weak and hurting too much to be following a conversation. About the only thing that would bring him around at this point was if either of them poked around at his chest too much. The pain that caused would send him shooting awake in an instant.