The bones of the head do sympathetically vibrate on the upper pitches, and this is why we have the term “head resonance” – a feeling of bone conduction of vibrating air molecules. This does not enhance our sound to any appreciable degree the lower we go.
The bones of the head vibrate due to the air that moves through the decreasing size of the glottal slit which fills up the sinuses as one sings higher. The direction and feel is literally back, up, and over. This resonance is important as far as the feel indicating that the registration, and vowel size and shape, is correct. It would also be important as far as adding a unique “flavor” to the sound due to physical differences from individual to individual.