I don't think there are any mods that make it automatic. But doing so wouldn't be terribly hard. You'd just have an extra php file with the requirements in functions set to give the award to the logged in user, and require it in the header. It wouldn't need to make any calls to the database until it was actually assigning an award, so the additional server load ought to be teensy.
I follow you, but I think your plan would indeed have to assign the award - it might be a better idea to have some kind of scheduled batch script that bulk assigned awards nightly, to take away any potential effects on performance (as well as to keep our code clean).
In truth there are a load of different ways we could go about it if we wanted to write it ourselves.
Perhaps instead of worrying about it now we could implement that functionality after a trial period with one of these manual awarding systems.