Using group policy, your machine can be configured to not allow USB drives or other sorts of revmovable memory devices. The use of such devices can also be tracked.
There are also many network management tools that allow the blocking and tracking of all that goes on on the office computers.
If it is against policy, there are probably allowed exceptions, and if your need is as innocent as you claim, there should not be an issue.
The thing to remember though is that these are not your computers, they belong to the company, and the company has the privilege of deciding what does and does not occur on those computers, and the operating systems of today offer your company vast and powerful tools for ensuring you do not act against policy and that if you do, they are informed of it.
UPDATE response to comment:
Group policy and any good monitoring tools will report whether the LAN is connected or not. They will simply save the logs until when they can transmit them back to the administrators.
Your best option is to talk to your supervisors. Any good sysadmin will not be fooled by your methods of circumventing their protections, and even if you successfully hide what you're doing, the fact that you're hiding it will probably not remain hidden and will raise suspicions on it's own. Let your supervisor know, then when IT asks why you did what you did, your supervisor will be able to tell them it was with his permission.
A good sysadmin will find out. You should work within the structures defined by the business unless you really don't care whether or not you get fired.