if you run a live cd, you can easily wipe out the hard drive, or read the contents of c:\documents and settings which, in the insecure windows world, contains a local copy of every user's files who have logged in.
so, you'll be able to access other users' files, format the hard drive, install viruses or spyware onto the machine, change the administrator's password, anything on that 1 machine. while it may not affect the network, it can still negatively affect that machine. I really doubt you will, or should, get permission.
now, if the school were to install a wifi network, and you were to bring a laptop, that would be good.