I'm using GameCenterManager from Apple and I would like to know if there's a way to disconnect a game center authenticated user...
Apple documentation says that,
After authenticating their account on a device, that player remains connected on that device, even when the player switches to other applications or reboots the device. A player only disconnects from Game Center only by launching the Game Center application and explicitly signing out.
See : Apple Doc.
So I guess no, User must switch to Game Centre and disconnect their self from there.
Potential reason : Game centre serves to all game apps which supports game centre feature. So, it's better to centralise a gamer's id. Same id for all different games. Now in order to do that they must authenticate gamer from one gaming device and maintain the id in all other application as well.
Now, if you explicitly disconnect from game centre from your app, the user will get confuse when he/she goes to another app and try to upload the score.