PuTTY SSH config

Yes you can! But it's another path where the Putty settings are stored. Where exactly the Putty configuration is stored is system dependant, but you can use a PuTTY session name just as if you would use a hostname for ssh to use that with git, at least with the git port for windows. That way you can set the auto-login user or other session features with the PuTTY client, save a session under a name you can remember and use the saved session name as a git host.