Actually, yes it is. Don't know about Xcode 3, but since you are a paid developer, you can get Xcode 4, and from there you can get Game Center API documentations. Here are the steps to do it:
1) Open the Xcode Help.
2) On the top you should see a navigation bar, which should say "Xcode 4.0 Developer Tools Library > No Selection". Click on the "Xcode 4.0 Developer Tools Library" section and move your mouse to where it says "iPhone OS 4.0 Library".
3) Now, move your mouse over "Networking & Internet" and click on it.
4) You now should have a list of available APIs.
After that just look around for the APIs you want, like Leaderboards, and achievements.
Just so you know, there is no single "Game Center API Documentation". They are all over the place. The main ones you are looking for are things like GKLeaderboards, and anything else you are interested in. Those documentations should link to other documentations you would need.