i honestly don't know if you can use a 3rd part USB lan adaptor or not...
BUT, you CAN use the Nintendo WiFi adaptor thats used for the DS. It just plugs into a USB port on your PC. run it, configure it. have the wii look for the Adaptor, Set access to granted for the wii through the adaptor on your PC, and your done.
thats what i'm doing. We have wireless here in the house, but my room is made of concrete, and i get HORRIBLE reception in my room. so far, the USB wifi dongle is working pretty good.
Eh, Just another option for ya.