Sure, in a manner of speaking. You can set different profiles to automatically run a console application, so setting one to "ssh user@host" gives you a profile

Sure, in a manner of speaking. You can set different profiles to automatically run a console application, so setting one to "ssh user@host" gives you a profile that starts a given SSH instantly in its own tab. I've been doing that for over two years now and I wouldn't go back to PUTTY for anything. Especially since the latest OpenSSH for Windows supports Yubikeys; the version Microsoft provides officially is a bit too old for that but if you use Chocolatey or download from the OpenSSH for Windows Github area you get a version that absolutely does work well.