We-eel, yes, it could be possible on a chumby One. Though it requires modifying the startup script.
Mount / as rw, and add this to /etc/init.d/rcS.background at around line 360:
mkdir /mnt/usb && mount -tcifs //192.168.1.6/share /mnt/usb -ousername=foo,password=bar
Obviously, change the IP, share, username, and password.
What this will do is actually quite interesting. If you plug in a USB drive and reboot the chumby, it will mount that as /mnt/usb and nothing will change.
If, however, you start up without anything in the drive, and if it boots up with the network connected, then /mnt/usb will be your Windows share. Even more interesting is that the "debugchumby" script is evaluated sometime after this, so you could create that file on your Windows share and get it to automatically start playing something.