This was what Tim Mills had to say on the subject:
I don’t want to upset all of the guitar makers, but this reliance on the body timber as being the whole source of the tone is a complete misnomer. My understanding of it, which is based on my own investigations and also having worked with some of the better luthiers in the country, is that the guitar’s voice comes from the pickup. The feel and the resonance and the sustain are a combination of body timber and body construction.
“With pickups, I believe that if you can find the right voice with your guitar pickup, then you will really bring out the best in your guitar. After all, an electric guitar without a pickup doesn’t work. The pickup is the guitar’s mouthpiece; the pickup hears the sound of the strings, but equally the strings are reliant on factors like the timber and the construction as to how resonant they are going to be. That’s when the importance of timber comes into it, but the ‘voicing’ is down to the pickup and how carefully you choose the materials. As with all of these things, it’s a combination of the whole.”
I also disagree with Tim here. I have two identical guitars, with the exception of the neck wood - one is mahogany and the other is pernambuco. My wife, a non-guitarist, can hear the difference between the two when played by me back-to-back through the same rig.
Based on my "research", guitar wood DOES affect the voice of the instrument. Paul Reed Smith agrees with me too, and he likes to use the following example.
"Guitar pickups are like microphones, they transfer the voice of the guitar. No matter what microphone you put on Barbra Streisand, she's not going to sound like Paul Rodgers, right?”
