Poindexter
Minister of Fire
Chemist here. Actually, that is quite a thing. Coal combustion mostly leaves carbon monoxide as the primary combustion product, not carbon dioxide. That's why it's so easy to kill yourself by barbecueing indoors. And carbon monoxide has a lot of BTU's that are released when the cat combusts it to carbon dioxide.
Back in the day, "city gas" was not methane as it is today, but carbon monoxide. They powered street lamps with it, and people cooked with it. Quite dangerous, but without alternative at the time.
So, TLDR, the coals indeed give a lot of food to your cat.
Good to know, biologist here. So will any old noble metal catalyst be able to do this, heated to only +/- 600dF?
When I was burning hardwood lump charcoal in mine the needle on the cat probe didn't move when I closed the bypass door, I got it up into active with the bypass door open, and then when I closed the bypass the needle didn't move.
I think I remember without a catalyst there needs to be an oxygen rich chamber with plentiful oxygen and lots of turbulence to convert CO to CO2 at or near 1400 dF.