Note that I'm not talking about the default gateway going down or some failure like that. That's the reason I brought the wireless scenario. The fact is our windows users can unplug their laptops from the wired LAN (the "staff" network) and move around the building without having to restart their network interfaces (the wireless network is part of the "students" LAN, a wide-open insecure separate LAN). Our Linux users can't.
Don't know about the routing failover, but I'd say have the DNS in the staff network consult the DNS in the student network for just that zone. You can put a cheap NAT router in that path to prevent other traffic from getting back onto the staff network. As long as you're plugged in, you get DNS from the staff server, and indirectly from the student server for just student host queries. Disconnect and you only get DNS from the student server.