Yes, depends on the locale for how risky this is, but I fully agree with my comrades that are recommending a crappier bike. Pick something up at a co-op or post a WTB in the for sale section here for a cheap bike boom bike that uses a derailleur claw. Those are excellent candidates for single speed conversions. This 520 will just get beat up and/or stolen. It sounds like your daughter would take good care of it, but commuter duty is rough on bikes no matter what you do.

I'll also add Trek is a well known bike name to folks outside our hobby and to thieves. That and Specialized would probably be the most well-known bike brands in the US. Doesn't matter if it's vintage, that name will attract theives. Anonomizing would help, but I don't think