|So the Verizon Wireless Network Extender is a cell phone network extender not a wi-fi network extender. Thats fine then.|
To make it work you need to find out of the wall socket is providing a DHCP address from the collage's router.
If it is then just plug into a switch and the witch into the wall socket and it should work. you can tell if it is DHCP enabled by just plugging in you computer, rebooting and the go to a command prompt and type ipconfig /all.
If it is a private DHCP address in the range 192.168.x.x. or possibly 10.x.x.x then you should fine. If it is a static IP address or a public IP address the it wont work.
Either way, I would first check that with the campus Admin as to what you are proposing to do don't fall foul of any acceptable use policy. They may not like it if more than one device is connected to each outlet and they can tell.
BTW: A device does not have to be a router to be WI-fi capable. A Wireless Access Point is not a router, but in your case would definitely fall foul of the rules.