The electric gtr is a very complex instrument, but what really counts here is human perception.
What is "sound" anyway? (The answer is 42).
When discussing tone we use terms like "air", "bite", "bark", "choke", "ice-pick", "woody", "sweet", "cream" 2 name a few.
EVERYTHING in the gtr is involved in creating these impressions. From the bridge type 2 the nut, from PU 2 the volume pot.
The way the neck is connected, 4 ex. will impact the pitch variations when we play. Twang a strat and gently push the neck 4ward - it will change the pitch. A Les Paul custom will just raise an eyebrow @ the monkey attempting the impossible. Maple fretboards will produce an "even" tone, the rosewood will produce "Stratititis".
The whole bloody thing resonates, mechanically and electronically. So everything affects everything.
Since most of the gtr's mass is made of wood, it will determine most of the mechanical resonance of the instrument, which in turn will drive dominant FQs within the string. That's the "sound" we hear when the amp is turned off.
When the amp is kicked in, the electronix resonance and side effects r added. Even the sound from the amp is picked up by the gtr's face which resonates.
The PU sits on a piece of wood that "moves", so it vibrates 2 in respect 2 the string.
So yes, wood plays a major role in the gtr's sound.
Having said that, my Strat is Mexican, and sounds gr8. I pulled out the original PUs though, the same day I bought it.