I don't know for sure but I wouldn't count on it. We were exchanging vouchers, not upgrading tickets, but money was still involved because we added Max Pass. I recall needing to show ID and sign an agreement of some kind. Often when contracts are involved a parent needs to sign, and since they look at ID they would know she's underage. I don't know if we had to sign an agreement because of the payment or just because we were setting up an AP. If it turns out there's a problem with her paying without a parent (but not with her collecting the AP), then assuming the ticket doesn't expire any time soon you could buy her an AP voucher and use the ticket for someone else to upgrade on your next trip.
I think you should call and ask. Maybe there's some way for you to sign the necessary documents ahead of time or authorize her friend's parents to sign for her.