Of course it makes a difference!! If not then you'd not likely hear any difference when picking up the same model of guitar for a start yet with the same pups, bridge, nut, tuners, scale length and strings, a guitar can sound different. It maybe subtle, nuanced etc, especially clean, but when you turn the gain up to distort, dial in your amp, EQ your sound and whatever else you do to change the sound to get the 'tone' you want, the subtle nuances maybe 'lost'.
Also, when it comes to 'Electric' guitars from a Musicians perspective, they can't often change the woods to see what difference it would make - therefore dismiss 'woods' as its not really something they can change. They can change things like Pups or Strings, nut, tuner or bridge and if that doesn't work for them, sell the guitar. Therefore 'woods' don't matter to many - its not something they can change and doesn't matter because their Pedals, amps etc will 'change' the Tone to what they want anyway...
But as a Simple' experiment, try putting a Rosewood neck on a Strat for example. An identical carve, identical fret material, identical nut/tuners. Keep the same strings, bridge, body and pups - and you'll notice a Difference in the Tone - both unplugged and plugged in Clean. Therefore the woods have 'changed' the Tone.