Pretty much impossible as you stated. Plus any live coals will be smothered by the ash and lack of oxygen.
Agree about the symptoms, classic carbon monoxide poisoning. But. No, live coals will not be smothered by the ash. A pile of ash after the fire is out will be hot for a couple days. I have a burn scar on my ankle from stepping in one several days after the fire was out. Lid on might smother the coals but it will take awhile.
Harry K