Are there any p-style pups that have both coils pick up a string, say A on a 5 string? Or would this unbalance the output volume between strings?

If two coils picks up the A string, then the A string will be louder than the others, period.
Strange question though, what do you have in mind ?

Not to mention that the reverse polarity would cause some loss of high end on that string alone (similar to a normal humbucker pickup).

Well I saw the 2008 B55 ESP-LTD (the old one IIRC had black hardware and JJ pups on the 5er, the new one has chrome hardware and PJ on 4 an 5) and the P pup (passive ESP) has both coils picking up the A string, apparently. Since it's in a closed housing, I'm guessing the pup is blade-type, so it's reasonably wide inside the casing.

The reason why I was asking is because my current builder wanted to put 4 6-string soapbars in a dual P configuration, with every pair picking up the middle 4 strings with both pups, and I obviously said I'm not comfortable with that, since I never seen it before, and frankly I don't trust his experience in that matter (haven't told him that though).

You'll ask then "why did you go to him if he ain't that good", well he's currently the only one in the country doing this sort of stuff, and while he's not an electronics genius, not by a longshot, his craftsmanship is very good, and he makes me an 8-string with custom string spacing, neck width at nut, neck profile, extended fretboard, 36" scale, with my body design for less than a quarter of what established builders would be asking. So I'd rather have a good hunk of wood, since electronics are swappable.

Anyway, I was asking just to make sure, cause 4 6-string soapbar routes mean a LOT of wood wasted and a lot of holes to cover in case it doesn't work out. So I think I'm gonna have him put 4 4-string Jazz pups and wire each pair with series/parallel switches for more versatility.