Yes, there is a 10% admin. fee. That is irrelevant to the EV of the BBJ however. The EV is a function of the likelihood of hitting the JP in any given hand, the average JP rake per hand at a given limit since not every hand is raked, and the amount of the JP (which is not constant - it grows until it is hit, then it starts over at a much lower amount.)
The qualifying condition is quad 2s or better beaten, but it also requires at least 4 players to a flop. I have no idea what the tipping point is to make the JP +EV, but IIRC BW calculated the tipping point of the Party JP (with quad 8s or better as the qualifying condition) at 170k at 2/4. The tipping point for the AP JP is presumably considerably lower.