Before we dive into it:
Does wood make a difference in an electric guitar?
Let’s put it this way, If you take a Lamborghini engine and put it inside (let’s say) a Ford Fiesta, it will not be a Lambo, right?!
The guitar body and neck are the chassis for the pickups, yes, each pickup has its own tonal characteristics,
but that chassis will make the pickups behave in a certain way.
It’s a “closed circuit”, each string has its own amplitude frequency and the guitar components must react to that amplitude,
for instance, if the neck is too strong and has no flexibility, you will end up with wrong overtones or none at all.
It has nothing to do with the pickups yet, that is just pure physics.
Each wood has its way of picking up the strings’ vibrations and transmitting them back to them and then back to the rest of the components.
The end result is what the pickups will pick from those vibrations, therefore,
if the vibrations are incorrect or intersect, you’ll get a shitty-sounding instrument.
A good instrument is one that once you strum it, you’ll feel the vibrations going from one side, all the way through to your hands and back.