I do have to shell out about $200 for her to join, so there is a buy-in.

It isn't that she will cry if she loses--she's a good sport generally--but if her opponent gloated or made a big thing out of it, she might. I don't know what the culture is likely to be. She has never been in anything competitive before. We are new to the school, so I don't know anyone else with a kid on the team (I am not even totally sure about how the club vs. team thing works anyway, but my guess is that if DD can join the team, she will want to).