Having said all that, it does not manage ssh keys.
And, of course, iTerm2's multi-window tmux integration, session recovery, and password management are mostly intended for use over ssh. It has a built-in file upload and download via scp. It will optionally report and graph bandwidth used over an individual ssh connection. It automatically lists (under Profiles) ssh hosts on your local network if they are running avahi/bonjour and sshd, and will even connect to all of them at once with a single click. So, my answer is 'yes', because iTerm2 is very ssh-aware. On OSes that come out-of-the box with ssh (ie macOS, Linux, OpenBSD and FreeBSD), client software that re-implements the ssh layer is rightly viewed with suspicion, and software that is simply 'ssh aware' is more common.
On Windows, in the old days, SSH wasn't built-in, and clients like Putty had to implement their own ssh layer. I guess that depends on how you define 'SSH client' from a user perspective.
But is it really an SSH client? Isn't it just a (very nice) replacement for Apple Terminal?