Not really, the game has to contact the central servers to update your medal counter and compare it against other people's results, obtaining the ranking which you can see above the race selection menu. It must been using a tiny amount of bandwidth, but it's being used.
-Lashiec
Ok, that would make sense.. But either that list is REALLY big, or they are downloading a HD movie displaying a bright medal spining, because that wouldn't account for 300MB of bandwidth after a few hours of single player gaming

Actually, after further investigation, i have found out that the p2p network is used for distributing the avatars, the custom paints and cars, etc etc.. Thus, it is as active when your playing the single player game as when you're playing the real game. Nevertheless, i think it should have a warning somewhere.