Unless you have some kind of dedicated high-speed direct link, the latency from that would likely be horrible enough to make any games unplayable. In any case, IIRC most remote desktop schemes need admin to install.
Like freakichu mentioned, if you're allowed to boot to portable media at your school, I'd go with some kind of live Linux setup. LiLi's nice for doing those on flash drives, (super user-friendly, it even auto-downloads your chosen distro for you), and it also has a way to setup Linux with persistent storage for your install, so you wouldn't have to re-install things like java on every reboot. You'd essentially have your own computer on a stick. This path becomes all the more plausible if the computer has USB 2.0 onboard. Either way, even if it's a bit laggy because of the I/0, it's miles ahead of trying to use a remote desktop for gaming, at least in my experience.
(You could also use a portable hhd for this for more room, and if there is a SATA port on the computer, (often combined with a USB port), you could likely get near-full-speed I/0 to it.)
Link to LiLi; http://www.linuxliveusb.com/
EDIT: I forgot, it even automatically does virtualbox setup on the stick too. That might be an option if you aren't allowed to boot to your own media, as long as the computer can handle the overhead, but it's also just plain cool.
:iia: