Closed/isolated local networks like you are talking about are common within industry.
I assume you want to connect devices wirelessly. You set up the TC as a router (probably the factory defaults) and create a wireless network. Just do not connect its wan port to the school's network. The amber lights going to flash, but it should work fine otherwise. All your devices will log into the wireless network provided by the TC, the TC will give them local IP addresses and they should be able to connect with each other via typical sharing arrangements (they all should see the internal TC drive if the TC is set up to share the drive). At your PC, you may have to manually switch between internet and this local wireless network depending on what you are doing.
If the desktop PC is hardwired to the school Ethernet, you may be able to configure the PC to share your internet connection with your wireless devices. I dunno if you can also transfer files between devices sharing that connection. Some times the PC security settings won't let you do this... and usually VPN will be disabled when sharing the connection. Do you own the desktop, or is it under the control of the school's IT dept?