While it's always worth asking (the worst answer you can get is a "no", and SMs are a helpful bunch who will often give you a "no, but": "No, but you can shadow me on another show"; "No, but maybe next season"; "No, but I have a friend at the Swan Theatre who could help you out"; etc.), I would encourage you not to get your hopes up.
Dance competitions, especially those with young contestants (13 or younger) are frantic and hectic and crazy and (IMO) an awful lot of fun to work, but in general the organizers don't want too too too many unknown people backstage because of good, old-fashioned stranger danger. It's usually hard enough talking them into letting us post male technicians backstage, and our guys are full-time staff who we've known for years. Posting complete strangers backstage would not go over well. (Mind you, they seem totally okay with women. It's the men dressed all in black who make people freak out.)