It would not be expensive or difficult to have a software routine loaded by the school to do such monitoring.
In fact, if in the simplest form if you just wanted to view the person while they were logged onto the school web site you could write that program in under an hour.
Remotely activating a web camera dump while the student has the computer on but not on the school site is only slightly more complicated. The school knows the MAC address of each laptop and that is a great starting point when doing anything remotely.
ha, true, you might be able to do that but not any random person working at the school. If the school did do this it isn't the assistant principle acting on her own. No, the school would have put out bids and done the job by the book, and yes, it would be expensive. That is how public bureaucrats work.
PS. I am not saying it is impossible or even difficult to do, just unlikely, considering the obvious potential for abuse.