Personally I think that one should always try and work with SysAdmins rather than pushing against them. There are all sorts of reasons why systems are set up the way they are, and why there are particular restrictions, that are not always self evident to an end user, particularly a pupil at a school.
I agree with audiovoodoo that the best policy is to try and persuade the admins to set up a separate Linux PC rather than trying to run an unauthorised copy of Linux on one of the Windows machines (particularly since Linux would give full access to the Windows partition).
Apart from any other argument, gaining unauthorised access to any computer system, which is what is being suggested here, is a criminal offence in most countries - it certainly is in the UK.
I know that I sound like a boring old fart, but sometimes when has to work with the system rather than against it.