I'm on a network that doesn't allow Apple computers to connect through the internet because the IT people can't regulate the software on the computer.
Nonsense! all an Apple is is an overpriced PC You know that it is 100% compatible with your network so you must accept that that compatibility works both ways. I actually doubt if your IT people detected an Apple..................they saw an unauthorised piece of equipment. I am sure that if you read the small print you will find that all unapproved equipment is banned. This is a very common and sensible network policy. Why.............................?

1. Unauthorised equipment can contain all sorts of viruses, trojans, spyware etc.
2. It may contain illegal, unlicenced software. On their network, on their premises they would be liable.

Obviously this applies to ANY laptop or private equipment (which would include routers and proxy servers).

In answer to your "hypothetical" question: "yes" it would be possible but not recommended. You are on your "first strike", they know that you have the damn thing................they are watching you and waiting.....................

If I were you I would learn how to use a PC............

Think about it, if you want to use your Apple, get your own private connection