what I'm basically asking is, if your institution has content control on the internet, can you hook up a mobile phone to the computer and use it as a wireless modem... thing?
It's called tethering, and some phones are capable of doing it, but it also depends on the phone's wireless plan. Unless it's explicitly included in the plan, tethering is not always considered part of the plan's data usage, and additional (and highly exorbitant) data charges may apply.
Check your phone, and check the plan you're on.
Most recent Blackberries and Android devices can do this, and the iPhone is capable of acting as a wifi access point. If you have a smartphone newer than 3+ years old, it's almost guaranteed to be capable of doing this from a hardware standpoint; the limitation will be the wireless plan, and (in the case of the iPhone's AP functionality) having a wireless NIC in the computer.