+1, look at all the people that moaned about 4.1 breaking their 3G, it'd be that all over again. if it can barely handle 4.1, it can't handle game center.
plus the device is 2 years old, all companies stop supporting older devices, just look at 3.0 on the 3G not getting voice control and making videos, etc and the OG iPhone getting even less.
The point of GameCenter is to be able to play a game with someone else around the world in real time, can you imagine how much it would suck if I have to wait for the other persons iPhone 3G to load a game wile I'm on my iPhone 4.