My company lets us work from home sometimes using VPN (during weather emergencies and stuff). When logging in a big window comes up that says the network is private and for employees only and that there's no right to privacy while using VPN. It makes sense that they don't want people poking around their network but I wonder if the company can use the connection to look around my computer while I'm connected. I'm not entirely computer-illiterate but I'm not a networks person at all so the technical documents I've found don't help me. Is that possible, and if so to what degree?

UPDATE Thanks Mark. The funneling thing is what I was really asking about. Mostly I was worried that I would already have some IM conversation open or log into eBay forgetting that the VPN was open and that my company IT people would see it or that they would log my eBay password. Thanks again.

ANOTHER UPDATE What if my son wants to play online poker or Warcraft etcetera while I have VPN on to work? Can my company think I'm the one playing if I am not typing often?