Does not for me, not even with busybox sh and no funky escape codes in PS1 at all. It does with cat or yes running, so just something being output is not the problem… Hm.
So you're saying 'fish' intercepts it on the far end? The ssh server on the far end shouldn't be sending it to 'fish' until it knows what's coming next.
Is this a current-ish version of OpenSSH or some other client/server?
EDIT Interesting! I tested it with fish and it does indeed intercept it! Wonder how that works.