If you are trying to use your companies internet without them knowing than you are making a mistake if you think that this will cover your tracks.
First off the company will know the instant you plug your computer into the network. They may not see it right away but if they check their monitoring programs they will be able to see that there is a non domain computer on that network. No big deal, you're not busted yet. However, you are still connecting to their network and all your IP traffic is still flowing through their equipment, this means that they will still log every single thing that you do through their IAS server or through whatever they are using to monitor web page visits.
The first thing they will do is try and narrow your location down. You'll prolly see some of your IT guys walking around aimlessly, going into peoples office based on the scope of the IP address that has been assigned to your home computer. Eventually they will come into your office and see your non compliant machine attached to their network and more than likely this will flip their ****. If you work for a government agency, depending on what you're doing, this is punishable by up to a 25k fine and some jail time. Bottom line, don't do it you're only asking for trouble. Pleas trust me on this as these other posts, as knowledgeable as they are, are misleading you into thinking you can get away with this.