Can my network administrator know that I am using a virtual router to access the internet on my unauthorised devices?

Yes, your use of a wireless hotspot can be identified using a wireless intrusion prevention system.

The primary purpose of a WIPS is to prevent unauthorized network access to local area networks and other information assets by wireless devices. These systems are typically implemented as an overlay to an existing Wireless LAN infrastructure, although they may be deployed standalone to enforce no-wireless policies within an organization. Some advanced wireless infrastructures have integrated WIPS capabilities.

Besides physically running around and detecting hotspots via WLAN traffic ("warwalking"?), or maybe using the existing router to detect then, traffic patterns can also be a giveaway - your hotspot has a different signature than your device.

Instead of working against your sysadmin (which is a PITA for both sides), talk to him. I don't know why they have the "one MAC per student rule", maybe they can relax it a bit? Say, "two or three MACs per student". Not much more trouble to administrate.

I don't know how the political side of the student representation works at your uni, but often students can voice their interests in some way. Yes, this is slower than just setting up a hotspot, but also more effective.

I used to work as a network administrator's assistant for a college. It sounds like a generational difference issue or the school's network can't handle more than 1 device for each student, staff member, etc. Probably every student has more devices than the policy allows.

The short answer is YES they can detect unauthorized access. NO, don't do it. I routinely revoked access for network violations (file sharing, illegal software, viruses, porn in the computer labs, etc). Many of those students had to leave school, because college is quite difficult without computer access. The students are exposing the network to risk. What if someone's unauthorized device passed a virus that wiped your doctoral research and thesis? If you think it's a joke now, try it at a job and see what happens.

Work with the network administrator, student government, administration, etc. to get additional wireless access for "your other devices" that don't NEED to be on the school's network and/or in common areas (like the free wifi in most coffee shops). This prevents load on the "actual" school network, and still gives you the internet access you want.