Emancipation - S5-E8
Continuity mistake: At the very beginning, House walks in and puts his cane on the table on top of Thirteen's papers. She picks it up and moves it away, placing the bottom end on a stack of books. Cut to House and the cane is now flat on the table. (00:02:55)
Fidelity (aka: Truth or Consequences) - S1-E7
House: As long as you're trying to be good, you can do whatever you want.
Dr. Wilson: And as long as you're not trying, you can say whatever you want.
House: So between us, we can do whatever we want. We can rule the world!
Trivia: This episode contains another reference to Sherlock Holmes. Wilson tells the (fictional) story of who had sent House a present. Wilson says it was one of House's first patients called Irena Adler. He then explains that House had feelings for the patient, but did not take it any further and therefore regards her as the 'woman who got away'. Irene Adler was an adversary who bettered Sherlock Holmes - the woman who got away. As it happens, the fist patient House treats in the pilot episode is called Rebecca Adler.
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