So what you want to do is to put a public key into place without authenticating. Would you be happy if your uses did this and could overwrite the authorised public key too?
If there is a plain FTP server on each box you want to connect to and you have credentials that will let you FTP to each of them, then you can certainly script that to put the public key in the correct location.
Make sure that your don't overwrite the existing
authorized_keys file in case it's already in sue for something else.
Make sure that you get the permissions correct: mode 700 for
~/.ssh and mode 600 for files under
~/.ssh
Another way you might achieve this could be if you have a backup/restore agent on each, get the software to 'restore' your file to each in turn, but that might be more cumbersome that putting in your credentials in the first place and runs the risk of overwriting just the same.
I hope that this helps,
Robin