The ratchets would have different state yes. The MITM would mix in different entropy into the keys' states. It's only detectable if the MITM ever stops. But since the identity key exfiltration only needs to happen once per lifetime of installation (longer if key is backed up), the MITM could just continue forever since it's just a few cycles to run the protocol in the server. You can then choose whether to read the messages or just ignore them.

One interesting way to detect this would be to observe sender's outgoing and recipient's incoming ciphertexts inside the client-to-server TLS that can be MITM'd by users. Since the ratchet state differs, so do the keys, and thus under same plaintext, so do the ciphertexts. That would be really easy way to detect MITM.