Installing Outlet in Brick
I'll take a stab at this. I actually have on of these in my brick wall. Not the exact one you linked, mine is a Hubell MR420CZ, but it's very similar. I like it, like you said, it looks much nicer than the ones that stick out from the wall. It is a little bit clumsier to use, because the receptacle is actually recessed several inches in, and you probably couldn't plug larger plugs in, just the regular ones. So for example, a pressure washer that has a plug with built-in GFCI would not work due to the recessed setup.
Regarding installation, yes, the box is about the full depth of one brick, and about the same size as brick+mortar joints. I installed mine while building the wall. I suppose it should be possible to install into an existing wall, but it may be quite tricky.
The main thing is that, after making room by removing a brick and the mortar, you will need to figure out how to get the box in and fix it in place. With mine, I was able to mortar it in place and there are some screws that are now embedded in the mortar. You could probably use something like tapcons if you can find them thin and long enough and you have the right tools. You would have to be very gentle when fastening them. Or you could use a strong polyurethane based exterior caulk around the edge of the box. Depending on how the box you purchase is setup, maybe you will also be able to fasten through the back into the sheating behind the brick wall, if there is any.