Might be too tough to answer since it's so subjective, and the question might be more complex than it seems. Do you want to know how the P by itself will sound (that is, are you asking if it will be in an optimal location); how it will sound blended with the others; etc. The final result will be heavily affected by the quality of the pickups themselves.
Hopefully you'll find someone who's tried it. If not, consider trying this:
get a really really cheap J body (or any bass body with a fender style neck pocket). rout it to hold all 3 pups, and then transfer your parts over there to experiment with the tones. I'm guessing you'll have to rout partly under the pickguard and partly out of the pickguard -- so it's a permanent mod, for all intents and purposes. So you might be happier chopping up a throwaway body first before you alter your main bass. PLUS, you could do a complete open rout, and then play around with the positioning of the P...who knows, you might decide to nudge one of the
Js as well -- with a scrap body, you can experiment a bit, and not only decide how you like the tone, but exactly where you want the pups too.