I think this would theoretically work in the optimistic case. But it doesn't make a lot of practical sense: if the puck has the battery, you need to physically connect it to the headset anyway. Even if you used wifi for the data transfer, you're subject to any interference (retransmission of packets for a real-time OS sounds like a nightmare) and people leaving the puck on their desk and getting too far away. In a way, the cable is a feature and not a limitation.
Since it doesn't have a headphone jack (as far as I know) this is actually still a problem since you have to wear wireless earbuds with it, if you don't want other people to hear it.