I don't think it's possible to browse network shares using ActiveSync by itself. Lord knows, I've tried... and searched for any help on doing so. Nothing. You can do it with an ethernet or wireless network card, of course.
If you really, really need to do it, there is a (very buggy and unstable) commercial product out there,
Crosstech PocketLANCE which will let you browse network shares via ActiveSync, with the help of a server app on your desktop PC and a client on your PocketPC. However, the trial version's server app crashed my Win98SE machine at home without ever working properly, and caused my desktop at work to be very unstable. The product itself hasn't been updated in many months, and I'd suggest you avoid it unless you really,
really need the capability and are willing to shell out the bucks, cross your fingers and pray.
Going to set up an FTP server on my Linux box tonight and see if that works over ActiveSync. You could, in a real pinch, run VNC (freeware a la PCAnywhere), connect to your desktop, and use Windows Explorer to browse shares and transfer files -- but why would you want to, when you'll only be a few feet from the keyboard anyway? ;)
-Bill, Ottawa, ON