Specifically, if you bind authentication to the connection, then an attacker who impersonates the server (in this case because it's the first connection, but in other settings because they have a fake certificate), then client authentication is not portable to another connection, so the attacker can't mount a classic MITM attack. However -- and this is a big however -- that doesn't mean that there aren't serious security problems. For example:

* If you use SSH to copy a secret such as an API key to the server, then the attacker still knows the API key.

* If you download some file (e.g., a script) from the server and then trust it, the attacker can use that to provide a malicious script.