Does Minecraft only talk to it's online server to authenticate you have a premium account? Does it not talk to it after it has authenticated? Or does it do something else online?
In a blog post Notch talks about the problems his server is having. These seem to be purely related to the registration process. And possibly the downloads of the game.
When the server went down at the end of August/beginning of September the kids were able to play the game quite happily. There was also a "free weekend" where you could download and play without registration - again implying that it's only authentication.
Obviously, if you're playing a multiplayer game you will be in constant contact with the server hosting the map!
Your game gets authenticated when you attempt to start the game, and every time you try to join a server. I believe Notch has stated this is just to download your custom skin, but I can't seem find the reference for this.