Stagedooring does not equal fawning. It depends on how he acts. Granted, I don't know the girl in question, but I would imagine that, while fawning over an actor and ignoring your date would be a turn-off, respectfully thanking the actor and discussing the show while you wait would show her that you are a thoughtful, gracious person who appreciates the work that other people put in for your enjoyment and want to let them know.
There is also lots of waiting time at stage doors, particularly shows with large casts. You could spend that time chatting and getting to know each other, potentially extending your date by half an hour or so. Plus, you will have shared a really cool, possibly once-in-a-lifetime experience on your first date. How many people can say that?
All that said, definitely bring it up casually and gauge her reaction before dragging her to the stage door after the show. I am just trying to point out that it's not as terrible an idea as everyone else seems to be saying.
Nothing matters but knowing nothing matters. ~ Wicked
Everything in life is only for now. ~ Avenue Q
There is no future, there is no past. I live this moment as my last. ~ Rent
"He's a tramp, but I love him."