No; if it's a public school, the school isn't put in exactly the guardian position. Public school students have constitutional rights they can assert against the school. For example, the Court in New Jersey v. TLO said the 4th Amendment protects the rights of students against encroachment by public school officials. Additionally, you can think about it rhetorically by analogizing to religion: if public schools were temporarily "guardians," they could temporarily assert that schoolchildren change their religion and pray in school, etc. They could make medical decisions without parental consent.

This seems like a good article on the subject: http://www.ascd.org/publications/educational-leadership/dec01/vol59/num04/The-Right-to-Search-Students.aspx