I'm doing this right now. My 802.11b router started going flaky on me so I upgraded to a new G router to keep me going. Eventually I'll get a G card for my wife's laptop, but for now it is working fine with the old B card.
Check your router's wireless configuration if you have any issues. The G routers have both a backwards compatible mode where they drop the speed on all the cards down to 802.11b speeds to allow the slower cards to operate and a G-only mode where they ignore the B cards in order to keep the G equipment running at full the 54Mbps.