Does hashing an encrypted message suffer from any drawbacks?
Your scheme is of course insecure against any active attacks. B or another man-in-the-middle can just change the data and then calculate a new hash. This is why you need a MAC instead of a hash. And it depends on the method of encryption / hash if hash-then-encrypt is safe.

If anybody proposes such schemes you should try and use an authenticated cipher such as GCM. That will however still leave you vulnerable to protocol errors, so while you're at it: use TLS.