You might get some other ideas here on the forum, but I see no reason why you cannot drill a hole in the wall.
You will have to be sure that you do not drill into one of the aluminum wall studs.
I might go a different route though.
I would probably go through the floor behind the fireplace. That would put the cat-5 in the area that you need it.
There are most likely some wires already going through the floor in that area.
The fireplace should be easy to remove. I have done it on a couple of Bighorns.
Then you could add one of
THESE in the J-wrap.
Let us know what you wind up doing. And take some pics along the way.
Peace
Dave