Well, Jennings would be able to self-fund (to some extent), and I'm reasonably confident he would be able to fundraise.
That said, it would be very difficult to beat Hatch, even in a D wave.
Also, didn't Jennings live in Washington by 2006?
Orrin Hatch (R) 59%
Ken Jennings (D) 39%
I hate to say this as a massive Jeopardy! fan because Ken Jennings is literally my deity, but considering Hatch won reelection by over 30 points in real life, I don't see how a Democrat whose sole claim to notoriety was winning millions on Jeopardy! is gonna close that margin of victory.
Come on, the only reason Ken won the greatest of all time tournament was because he kept beating James Holzhauer to the daily doubles.