Adding a check if a user received the message yet would require at least a new field in the users table and another check every time he logs on. I think that's unneeded complexity there. If you don't want it to be spammed every time disabled the notification (there is a setting for it in the group AutoInv), and add a new topic or something similar telling your users the same.

The only case where this tell creates spam is on restarts of the bot with a large amount of users online already. That shouldn't happen that often though.

I would personally favor the approach of sending the tell whenever the person is first added to autoinvite.