Yes, it does. Minors do not have the same rights as adults (e.g. Amendment II). However, I think you'll find that, while the parents have the authority and responsibility to restrict a minor's freedom of speech, the school does not. This is just my gut feeling, though.
FReeper legal eagles: what say on this? Also could the legal strategy in the minor filing suit be that when decided it will be binding on all school princials and boards that want to try prior restraint?