Shadow-tx:
Welcome to the forum!
AS to your question.....energized tracks in the drawer?? I don't think so.
Thoughts on the matter are telling me whatever you may devise may not be NEC compliant.
If you have a hinged "door" (the front of the drawer), and the "drawer" is non-movable, you could mount a recept in there, and the dryer, shaver cords may be long enough to be useful.
Good luck, perhaps someone else has some opinions????
John