This would be just as easy with a small power strip. Drill a hole in the back of the drawer big enough to feed the plug thru and plug it in behind the dresser. Use 3M Command Strips or Velcro to attach power strip to inside back of drawer. More outlets and easier to find parts.
Wow! Never thot of this but would be so nice in the kiddo's rooms! Would give them more room to play and I wouldn't have to worry about bumped heads on those nasty corners! How To Build An In The Wall Space Saving Dresser