It wouldn't be unprecedented for the MVP to be a member of the losing team as it's happened at least once for each of the 4 major sports (NBA, NFL, MLB, NHL).
NBA: Jerry West (1969)
NFL: Chuck Howley (1971)
MLB: Bobby Richardson (1960)
NHL: 5 different times, most recently Jean-Sebastien Giguere (2003)
While I didn't witness any of them, it's tough to believe they could've done much more than what LeBron has for his team (and relatively speaking, I think no one on GS has even been playing at an All-Star Level and this is against a team of mostly backups outside LeBron).
I saw a couple of the Giguere games. Even as somebody who knows bupkis about hockey, I can confidently say he didn't suck.