I think the aging of the wood shells contributes minimally to the sound of wood drums. The main change that occurs with age is the shells crack and the staves separate, opening up a slight (or not so slight!) space that air can pass through. This gives the drum a dryer sound and decreases the bass, accounting for much of the "sound" of older wood drums in many cases. It can be "fixed" by regluing the staves, although many drummers prefer the sound of the cracked drums. The shell resonance (as opposed to the air column resonance) does not contribut a lot to the sound you hear, as contrasted say with a violin or acoustic bass, where the wood body is the main radiator of sound waves and plays a major role in the sound of the instrument. The sound from the shells when you play cascara on the sides of the drum with sticks does involve the resonance of the wood and aging may change that sound, but not in a major way.
As Marcus suggests, the major determinant of the drum's sound that may change with age is the skin. Many factors related to the skin may vary, including stiffness, thickness, density and flexibility at the bearing edge, as well as the tension on the skin (tuning). A well-chosen skin (not necessarily "premium") can be the second biggest factor in the sound of the drum. Probably the biggest factor in the improvement of the sound of a drum with age comes from ongoing development of the player's technique in creating the desired sound and avoiding undesired sounds.