Other mistake: House has Metroid Hunters on the DS next to the gangster's ear and it shows Samus in a ball rolling around. The way she was rolling couldn't have been achieved because House was holding it, his fingers nowhere near the buttons on the game.
Continuity mistake: At the very end of the episode, House enters the conference room and stands up in front of the whiteboard talking to his team. When he first enters, the board is full of writing, then in the next shot there are only a bit of marks here and there.
Answer: If he were caught, he would still be forced to serve the jail sentence he was given. In addition, he may be charged with various kinds of fraud: insurance fraud if someone collects on a life insurance policy, identity fraud if he gets fake documents, tax fraud, etc.
LorgSkyegon