I doubt there are a bunch of user accounts on a uni computer lab Mac, so this wouldn't be much different than regular screen sharing. It's also still a mess to choose which computer to try, doubly so if you're on an outside network.
But they could always just throw a beefy machine in a closet and have it connect to the same network directory service that the lab machines grab their user accounts from.
My old university did the same thing, but did so nearly a decade ago with a Windows terminal server.