No, it would not adversely affect the performance of your stove, as long as the pipe is inside the home. If it is outside, then it would considerably effect the draft which could be problematic. I doubt it would be worth doing from a mass perspective, but I am unsure if it would be worth doing from a cost standpoint.
You would save on the high cost of triple wall pipe, but that would be offset by the cost of the cement board and tile. So I am not sure.
If looks was not that big of a deal, I would just buy a roll of 24 inch aluminum trim, then some fiberglass electric
fence insulators, and some long screws. In that way you could stand the aluminum an inch or so away from the wall, then drive the screws through the aluminum, then through the insulators, and into the wall (studs).