NO. That is where the wrong touch comes in.
They cannot just randomly search students. They have to have reason.
Now, as a teacher, they can legally ask a student something such as "Do you want to show me what's in your pocket?" If the kids chooses to show them, that's on the kid. He could have said no. What's interesting is that the police officer in a school must have probable cause to search a student, a much higher level than what the school has to have. That's why you'll often see a principal with a police officer during a search and the officer will remain quiet and let the principal do the talking.
Lockers, desks, etc. are property of the school and may be searched at any time by school personnel because they are property of the school