There is no tag for the iOS Game Center.
Should any questions on it be asked here, or on https://gaming.stackexchange.com/ or elsewhere?
Or should cross-posting be allowed in this instance?
Game Center would be on-topic here since it is Apple software.
However, if you're asking about programming or developing for/with Game Center, that would be off-topic since this site is not about development. That kind of a question should go on Stack Overflow.
If you've got a question about Game Center that doesn't involve development/programming, go ahead and ask it here. I can easily make you a