I tried the exact same card with the exact same computer a few months ago. Long story short, it didn't work, but that may have also been due to the cheap Belkin wireless router I tried to use it with. Eventually, I somehow found an actual app for the Belkin card that brought up a very arcane and confusing screen that as far as I could tell showed the card as receiving a signal, however I still couldn't get anything to work. It looks like it's not directly compatible with the Airport networking standards, at least not on the B&W.
I ended up rearranging the network setup in the house so that the wired D-Link router I had was close enough to the G3 to be plugged in, and then I plugged my new Airport Express ($95 shipped and NIB on ebay) into one of the D-Link's ports and am running my imac G5 and mine and my roommate's ibook G4's off of that. We still have too much sh*t plugged in and running in this house, but at least there aren't cables running around on the floor anymore.
Don't know for sure what your options are. If it's the only computer you have, I would recommend trying to keep it wired, however if you have other computers that would benefit from wireless and can't set things up the way I have, maybe one of those wireless USB adapters would work. I don't know how those would function on USB 1 ports (which the B&W has), but you could also look into getting a PCI USB 2.0 card. That option may cost you a few bucks more, but it would probably be more reliable.
