We were able to successfully get an app into the App Store that utilized Gamecenter, but was not a game.
It is called Reminders with Friends. We used the turn based matchmaking in order to send and receive data (in this case reminders) between Gamecenter friends. We then use these reminders to set off time based or GPS based reminders. This was the first app that we found that was able to utitilize Gamecenter in this way.
If you have any questions, I would be happy to answer them.
Link to app: http://itunes.apple.com/app/reminders-with-friends/id486230629?mt=8
Link to website: http://slyceapps.com/reminders/