The wood does vibrate, but the extent of the vibration is small and surely couldn't contribute very much to the sound. (I have, however, felt the vibration in my fingers when playing a loud low E on Supercorders[TM] with the tone holes not yet drilled, so I can safely say the wood does actually vibrate!)
The area most sensitive to surface smoothness and moisture shedding characteristics is the windway, of which the exterior wood forms the roof. The smoothest woods focus the air column best. The larger (but still tiny) grooves of the grain of rosewood or purpleheart introduce a slightly different, but not always unwelcome, character to the sound.
The idea of "absorbing" windway moisture seems to me to be largely a fallacy. After some playing time, long or short depending on the temperature, the material around the windway becomes saturated and absorption slows to insignificance: essentially, windways must expel the moisture. Windways are not oiled, not because they will absorb less but because water would bead-up into larger droplets on oiled wood. The large beads of water are of course the chief problem with plastic recorders. The Supercorder's porcelain blocks are impermeable to water, but they have good "wetting" characteristics - water doesn't bead-up on them. (The glazed ceramic blocks I tried earlier were okay but not as good.)
But if the essential requirements for the wood are met (smoothing or oiling the bore, etc.), the wood is not the dominant factor in a recorder's sound. Geri Bollinger of Kng Blockfltenbau has suggested that the wood is like the canvas or paper behind the painting: it affects the painting but does not define it. He has made pearwood recorders specifically to sound like ebony and vice-versa, and he has suggested the following guide to the components that make up a recorder's sound:
Labium 30% [+ windway & voicing]
While one might point out the large difference a few strategic keys makes and debate about proportions, this certainly puts the role of the material into perspective!
In addition, perhaps half of the effect of the wood is owing to its being the material of the critical windway roof. With Supercorder, the beak including the windway roof detaches and can be replaced. A purpleheart Supercorder with an ebony beak will have some of the characteristics generally noted for each type of wood.