alt Hacker NewsSchool IT departments are unlikely to allow this. Even if they don't have technical restrictions, they'll have policies that prohibit it (at least my kids' school district would).
School-issued devices are generally intended to be similar to devices a corporation would provision for non-technical workers.
Honest question, if you buy (just a hypothetical, I assume most parents can't afford to buy one) a Chromebook for your kid that will be used in school, do you have to lock it down or can you enable the Linux system (assuming that you want to do that and that your kid is interested in learning to program).