Game Center requires wifi connection?

I just upgraded my Ipod Touch OS to 5.1.1 and have encounted the Game Center. 2 Questions: 1. Can I only play games using the Game Center? Are any of the game apps independent of Game Center? 2. Do I have to have access to wifi to play any games using Game Center? Since it requires me to log-in am I correct in inferring that I have internet access to play a game? If so, have I lost the ability to play games while on an airplane (or other spot with no wifi)? My first (and second) impression of Game Center is pretty bad--- I am not a social networking, share my game scores kind of guy.