I'm interested in limiting the use of a school network for academic purposes only. I would expect the solution to be able to efficiently filter and log traffic (to detect offenders) on an account by account basis.
Is this possible using the Raspberry Pi?
There are several vendors providing solutions that are doing exactelly what you need. I doubt that you can easilly achieve similar functionality from scratch using RPi as this is quite complicated solution that needs also apropriate hardware. In a nutshell you will need some advanced firewall with some fancy features like application recognition (to block choosen services) and URL filtering (or some HTTP protocol inspection) to have ability to block choosen URLs.
Try to find some open sorce FW and check if this will fit into RPi. Some example could be Vyatta.
Newertheless in my opinion without buying some ready solurion this will be extremely hard.
This could be achieved with a Pi, although one notably issue makes it an unlikely solution. The Pi only has one ethernet interface, and the kind of usage your describe is best implemented as either a router or a bridge containing two interfaces where traffic is filtered as it passes through from one to the other.
It is possible to eaves drop on a single wire and monitor traffic, but much more difficult to do anything about it. If you wanted to actually shape the traffic in any way, you would need to load the Pi up with another interface using a USB device and funnel all your traffic through it. Frankly I can think of other devices much more suited to this operation, including other one-board computers that have two ethernet interfaces out of the box.
