I hadn't really thought of it before now, but Thompson might have a bigger issue even if he declares after the current season wraps: re-runs. Even if the pld episodes featuring Thompson don't air on the NBC broadcast network, but they run anywhere from 1-4 hours a day on TNT and USA, and having to pull them over equal-time concerns would cost NBC-Universal, the studio with the syndication rights, a ton of money.
That said, I don't see (disclaimer: IANAL) how NBC can stop him from running for office -- UNLESS they have a specific provision in his contract where he promised not to run for elected office. In that case, it would be a straight breach of contract, and NBC could sue for the revenues they lost as a result. That wouldn't completely stop Thompson from running, but it could take a bite out of his campaign funds.