I think you answered you question by yourself
I do not want anything taking away from the pickup output or tone.
the interesting link from shobet explains that the JE-1200 adds on the mids lows of your tone....
Maybe it works with the jackson stock pups like the J-80...but as for me I really had a dislilke on that active electronics circuit (and also some issues with it).
But at the end, do you like your JE-1200 ?
Maybe you could decide whether to keep it or not when you'll see what's the result with a NB on your guitar. :D