While not much is impossible, it would probably be highly impractical. I'm basing this off of my own BO's preamp. I have the 4-pot, long-shaft version, but I assume the electronics are all similar.
The first problem you run into, is that all the pots are 25k. Not to mention, that the bridge volume is incorporated into the preamp circuitry. It would be almost impossible to isolate it. The 2nd problem is, I'm almost positive that the BO preamp uses balanced differential inputs. In other words, the red and white wires aren't shorted together. I just put a meter on the red/white wire inputs of the preamp connector, and they are, in fact, isolated.
So, the only way I could see for this to work, (and even it's awkward), would be to use a 4-pot, LP style guitar. Two pots would be the master vol/tone BO's circuit, and the other two wouldd be 500k passive vol/tone. Then you'd need a 6PDT switch to switch the black, red, and white wires of both pickups. Grounds could stay common.
Do-able, but not very practical. IMHO.
Edit: Examining it closer, the attached pot is easily isolated. But that doesn't change much else.