Is the top layer of block filled with concrete?
If not, you could fish a romex or better yet, some 1/2" flexible metal conduit
down through the block to where you want the outlet.
First you'll need to find a clear cavity from the top block all the way down
to where you want the outlet. Use a 3ft level and mark the wall, or use
a piece of string with a bolt or something tied to the end for a weight.
to make a make shift plumb bob. Drill a 1/2 inch hole with a masonry
bit in the center of the spot that you want your outlet to be.
Now lower the string with the bolt on it down the cavity inside the block wall
to where the drilled hole is. if it travels down freely, with no snags,
then you could fish an electrical feed down there. First you would need to
cut the hole for the electrical box. Use the box as a template and mark the
drywall. Cut through the drywall first. Then cut the block also to the size of the electrical box. I would use a 1/4in. masonry bit to score the outline of
the box on the block. Then finish the cutout with a hammer and cold chisel.
Now using the same string with a weight on it, lower it down into the block
cavity from the top of the wall down to where your box cutout is. You should be able to hook the string and pull it out of the cutout. You are now able to fish your cable or flexible conduit down to the box by tying the string to it
and pulling it down to the hole that you cut for the box.
Sounds much easier to surface mount it, just as you said.
But it could be done.