hyedipin, no it won't work. That adapter only works with 16-bit PC Cards, and almost all 802.11b cards are 32-bit cardbus.
I recommend getting a CF card 802.11b card. I just ordered one off
www.HSN.com for around $35 (including shipping). You can use it with a laptop with the included adapter (so you don't have to carry around 2 802.11b cards on trips.
Link to the card I ordered.