Even if that were technically feasible from an interoperability perspective (which in many cases it is not, due to them using proprietary software) a parent putting Linux on it would certainly violate the acceptable use policy when the school inevitably finds out. Consequences from there will vary dramatically, but none are likely to be desirable outcomes. At the very least, they'd probably tell you to either restore the device, or pay for the cost of having their person do it.

Parents don't generally own these devices and are not going to be legally authorized to install software on them, generally. In the US, for example, unauthorized access along with "damaging" the device by removing the OS could very well be a crime (or several.) I doubt it would be prosecuted, but I personally don't have money to burn on lawyers.

edit: to be clear, where I live, these systems are typically owned either by the school system, or by a third party leasing agent.

Yes, because the schools own and manage the hardware they loan out.