Do you know other computers that can connect to multiple networks at a time?
Once the printer is on the network, or the printer is connected to a computer on the network, and you have the system properly setup so that all devices are named and known, there should be no trouble. You may be missing a few steps that would be too long to post here, but there is plenty of poop availbable with a Gurgle search...
If the wireless unit is appropriately connected with the correct install software, and everything is properly identified, then what you want to do should work effortlessly.
You should be able to see all your networked components in your MyNetworkPlaces, with the printers also listed.