Re: the timbre of an electric guitar plugged in vs. acoustic, if the wood didn't matter, then they wouldn't be made out of different tone woods. Still, I doubt the sound of an electric guitar unplugged can be discerned all that much from the plugged in sound. To say that "it doesn't matter", though seems as dangerously ignorant as saying, "it does matter" when both positions are likely devoid of any absolute proof as is the case of most arguments that go on forever.
Also, the physics of the electric guitar circuit are amazingly complicated even though the circuits themselves are relatively simple. Each pickup is a coil which makes the guitar into an LCR circuit. Check out this Wikipedia link for the math on just the LCR aspect of a guitar (pickup/cap/pot). How do you fit "woodiness" or "chime" into those forumlas?
I will absolutely play an electric guitar unplugged before I even consider plugging it in, though. Why? Because I'm looking for a couple of things. They are: Sustain, resonance, and feel, all of which can be masked, altered, or massively overwhelmed by an amp. We tend to focus on the sound and feel of the amp when plugged in, and to Pascal's point, since that's all the audience hears and feels, maybe that's all that should matter, but as the player I get more out of playing when I have a good interaction with the instrument and for me that is best experienced when unplugged.
Example: I have a Fender American Deluxe Strat that I bought new back in 2008. I am not a Strat guy. I tried it in the store because it looked pretty and I figured I should have a Strat. One strum unplugged and I knew I had to have it. The feel, resonance, and sustain were all remarkable. I plugged it in and it sounded like... a Strat. I took it home, gutted the terrible noiseless pickups and S1 electronics and replaced it all with vintage-spec boutique parts and now it sounds MORE like a Strat!
Pics because I'm the pic guy:
Before:
Original vs. my electronics:
After:
Do I sound more like Mark Knopfler because of the unplugged characteristics of this guitar? Hardly, but I like playing it more because of the responsiveness and feel of the guitar and I can concentrate on those things better when I play it unplugged.