I'm going against the grain here. I've known pageant kids and I'd say it's very much a toss up on good/bad experiences.
On the pro-pageant side, a lot of girls really like this and it does actually translate into being at ease before an audience and building a lot of self confidence in terms of making a presentation of any kind.
On the anti-pageant side, parents (not kids) can get way too competitive and invest way too much emotionally in the events. Plus, you've got a financial consideration here, too.
I would say do it for the novelty and see how it goes. If she likes it, fine. If she doesn't, make her take piano lessons.