security - Can Juniper's Network Connect SSL VPN software access information on a Windows client PC?

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?

They can only access your computer as much as any other computer on your home network can. If you have C:\ shared to everyone, they could potentially see everything on it - though this is unlikely unless you have a sketchy IT department. Otherwise, you should be fine.

That warning is up because all of your traffic is funneling through their network connection. This means that if you forget to terminate your VPN session and go surfing for porn or torrents, etc - it will all be logged on the company's servers.

Connecting to VPN exposes you to "risk" from the side of your internal network. But there is much greater risk of being attacked from Internet. If you don't have evil enemies-hackers in your company and don't open up all the ports for all applications in the firewall then you should be safe :).