Even if the virtualized router is down, I'll still have access to the physical server over the network until the DHCP lease expires. The switch does the work of delivering my packets on the LAN, not the router.

Yes, of course it depends on your network topology. If you have a link in the same subnet you're good (and can configure a static IP if need be). But if you're using vlans you can get in a pickle if the router is down. In my setup everything on the user side is segregated so if the router goes down I have to take a dedicated management laptop and plug into the host management network directly on the management switch where i keep a port empty. This maintains segregation and in practices means I take my ancient Acer Aspire One used for nothing else into the server room that looks strangely like a laundry room and plug it in.