Thought I would come back in to add that this has intrigued me and I've spent some time thinking about and researching it. I found a discussion regarding optimally locating bathroom outlets and one was in the vanity drawer though it doesn't sound like a 100% certifiable solution:

"A designer told me the latest trend is to install a plug in the back of the drawer wires would lead to another box in the wall under the counter). The original box in the wall falls within code. At final installation, the box and faceplate are installed in the back of the drawer. You plug in your hairdryer and when needed, just pull it out - no need to ever plug/unplug."

And another though it doesn't describe the technical end of their solution:
When we remodeled our master bath several years ago, I had a deep drawer installed with a strip plug inside the drawer. This is where all those bulky things like my hair dryer & curling iron go. Out of sight but can be pulled out & turned on to use. Also, I wish I had had a second drawer installed for my husband & his electric razor & hair clippers. He is always putting them in MY drawer & getting the cords all tangled. We are now in the process of building another home & you can be sure there will be HIS & HER drawers."