im not certain on this but i think you should be able to go back and get any critical updates. i bought a new hard drive a couple of months ago and i was able to get all of the updates from service pack 2 onward, i dont see how your situation is any different.
you should probably also set up your updates so they install automatically at a specific time when no one will be on the computer, so whoever is cancelling the updates wont do it anymore.