However, when a student starts a VM from this template, it appears the network configuration is messed up. ipconfig only shows the NIC for the virtual switch, but not the "ethernet" adapter that's connected to the HyperV host. However, looking at the adapter settings I see the adapter is enabled. Routing and Remote Access does not list the adapters in the NAT configuration, wherass the template VM does.
My assumption is that something happens with the virtual NIC on the root/parent HyperV host when it gets created from the template.
You are allowed to use only one interface on the LAN. So, if you create an External switch (default setting) on the template, I assume the lab service, will terminate the Ethernet. You should use the Internal switch.
I'm not an expert on this but we are using Hyper-V in our labs with the Internal V-Switch and things work fine. But we also don't configure the networking in advance. We only provide the Hyper-V manager on the template and let students install the Hyper-V and configure the V-Switch.