How does a guitar body affect electromagnetic pickups?
I think the best way to think about this is to not only think about the wire (moving guitar string) cutting through the magnetic field of the pick-ups (stationary) but also to think about the pick-ups themselves moving with the resonance of the wood that they are fixated to.

Now you must consider the frequency response of the instrument as a whole and this would definitely be affected by the choice of wood.  How much it affects the sound is another question.  I personally believe the subtle differences end up being audible due to the degree of amplification.  But in the grand scheme of things, this is just a part of the entire signal chain that can effect your sound.