Governments already set up hoops and regulations. They control funding by interfering with schools. They control how teachers are motivated and their education standards. The government is stamped all over the schools. Letting the government be involved in potentially illegal behavior going on at school is not a foreign idea.
No, I think the government does not have the right to intervene in Internal school affairs for the purposes of drug testing. The privacy of the students should be a priority of the school they attend and allowing drug testing would violate this privacy. Therefore such testing measures should be prohibited.