With only one pickup active, the phasing does not matter and the hum level should be no different.
The time the phasing would be noticeable is with both pickups active at the same time. In or out of phase will give a different sound.
The hum will depend on relative winding directions of the two two pickups; it could either add or cancel to some extent.
(Swapping the magnet polarity would reverse the audio phasing, but not the hum - that's down to coil winding direction alone).
If the guitar is not already fully screened, it would be worth lining the pickup & control cavities, and covering the rear of the pickguard, with self adhesive copper foil screening tape. Link that to ground, it reduce general noise pickup to some extent.
The proper stuff is supposed to have a conductive adhesive but I always add some small solder spots at various places on the overlaps to ensure good continuity.