Convergent Encryption: integrity and authenticity
If you use the hash as a known key, then you do not need any additional authentication to ensure plaintext integrity. An attacker cannot find another plaintext with that hash value unless the hash is broken.
However, there are two problems with that:

Like MAC-then-encrypt the hash only ensures authenticity of the plaintext, not of the ciphertext. This leaves it possible for an attacker to use chosen ciphertext attacks and CBC implementations may be vulnerable to the padding oracle attack.

Typically in convergent encryption you have a longer term secret key that is used to encrypt many plaintexts, and the hash that is used as key for one plaintext gets encrypted for the long term key.
Unless the hash/key is encrypted with authenticated encryption, a chosen plaintext attack could allow an attacker to halve the hash space to 128 bits, for which collisions could be found. I.e. you probably want to ensure the authenticity of the encrypted hash, if you use this setup.


Thus, I would recommend using authenticated encryption the whole way through. If you are concerned about space usage, you can shave off some by getting rid of the IV. One-time keys can be used with zero IV.