Is it stupid to try to get a flight to the New York area just because I have a chance to go see a Broadway show for free?

Seriously, I'm sure I'd spend more on the flight than the tickets would cost were I paying. OTOH, I've never been to NY. I want to. Someday. Should I take this excuse? Of course, this would just be a short trip. And there is a chance I could get lodging in NJ. Am I crazy for wanting to try?