Having graduated from Princeton at age 10, it's possible that rulers of Panem might actually waive the '12 years or older' stipulation for Dr. Doogie Howser. The idea that brains are more important than brawn is one of the central themes of The Hunger Games, and if that's true, then God help whoever enters the arena with this medical prodigy.
However, his Hippocratic oath would have an impact on his combat effectiveness. He'd be able to patch up allies and think outside the box, but could he kill? If he ever did, the mental trauma alone would likely remove him from contention.
Odds of Survival: Fair.