The thing about coals is there is no cat food in them. Carbon combines with oxygen right about 600dF, just barely up in the active zone on my BK cat probe indicator, but since there are essentially no VOCs coming off the charcoal, the cat is hot enough to be active - but there is nothing in the exhaust plume for it to eat. A hungry cat so to speak.
You can try this with hardwood lump charcoal right in your stove. I did. Wood coals are wood coals are wood coals. Do not try this with briquettes. Briquettes have all kinds of binders (glue) in them, and glue is verboten.
I did ask
@BKVP I think two seasons ago if, when burning charcoal with an indicated active cat if there was measurable heat being produced combining carbon monoxide with oxygen at the substrate to exhaust carbon dioxide. I didn't hear back from him, but I suspect it would take some very precise intrumentation to find a BTU or two here and there in this situation.
In shoulder seasons a heap of coals might be plenty to keep the house at a comfortable temp. In colder weather an accumulation of coals is in the way of loading more catfood into the firebox,