Part of the difference between a J pickup, and P pickup is the placement on the body, while most J pickups do not have the low mids of a P, they do have lows that a P won't do because the J neck pickup is so much closer to the neck. With it's position on the body, in relation to the bridge/neck, it most likely will sound even less like a j neck pickup in parallel, it would lose those low mids, and lose some of the deep lows it has, where they are on the body, and being single coil, is what gives Jazz basses the somewhat scooped mids sound, when compared to a P bass. Besides the placement, it's the nature of a dual coil pickup to have those mids, having the 2 coils in parallel would effectively turn the P into 2 single coil pickups, each of which is smaller, and weaker than a single J.