Yep - that'll do it! Probably hasn't been noticed by the admins yet thanks to the weekend. Should still be in the grace period for renewal so they shouldn't permanently lose it. Plus being an .edu TLD gives them some protection as well.
Yes I'd imagine it's chaos there now. If the registration on their primary domain expired, that's going to take down their entire online infrastructure - web, email, dns, everything. They should have internet connectivity, but all incoming traffic routed through their domain or configured with the domain or subdomains (firewalls, routers, etc) is going to be cut off.