You would not need to use a sheet of plywood to mount every thing. You could simply place boards behind Sheetrock, but those board would have to be placed precisely where the TV need to be.
I would suggest building the wall a bit farther out to the sides of the fireplace, then forward of the brick face. If you use board, rather than plywood, then the wires can run between the boards, and exit the false wall behind the TV.
Keep in mind, before you close up the wall, all the wiring would have to be in place, and if you have to replace a wire, you might have to tear up the Sheetrock. Though equally, you could use the old wire to fish the new wire through.
A lot of things to consider.
If you have a new AV Receiver, then a single HDMI cable which will have ARC (audio return channel) plus the power cable would be about all you would need. For TV Reception you would need the antenna or a connection from the cable box. Today, most of these cable connections are HDMI.
So, using the most basic assumptions, you would need two HDMI and a Power Cable. That should be easy enough to place behind the Sheetrock.
If you placed a couple of horizontal 2x6's to mount the TV bracket to, that would move the wall forward by about 1.5" + 5/8", the moves the wall roughly 2-1/8" forward. The 2x6's could be solidly secured two the larger framework at the sides of the Fireplace.
You might be able to use 1x6" which would make the wall more shallow. Though in 1by wood, I would be more inclined to use plywood as it has a more complex cross grain structure and would probably hold screw a lot better than solid pine.
I suspect, though I can't know for sure, that the brick you see in your living room is cosmetic, and that behind that brick is another layer of less attractive brick that constitutes the actual chimney. But, if you drill into the brick, whether it is cosmetic or structural, you can't really change your mind later. Once the holes are drilled, they are drilled. The next person who lives in the house might be less than satisfied with holes in his chimney. That makes the False Wall more attractive. If the next owner doesn't like it, it is not that hard to tear out the false wall, and have the clean unblemished brick newly exposed.
Just a few thoughts.
Steve/bluewizard