In theory, yes, of course (CO). In practice, I am not personally aware of any deaths from that, but the continuing use of heavily coated "tents" by the US military is certainly going to create "opportunities" for people to gas themselves to death - I see those are turning up on the surplus market, so some elk hunter somewhere is going to fall asleep in one of those on a cold night with a couple of burners running... it's inevitable. But it seems unlikely in a backpacking tent or traditional canvas wall tent. In those, fire is the big danger.

IMHO, the biggest "fume" danger is from fuel vapors, like from a white gasoline stove, and ignition of those have for CERTAIN caused nylon backpacker tents and contents to burn nearly instantly. Having said that... most of my personal in-tent stove use has been with white gas backpacking stoves. Gotta follow good rules... tents used to come with a "stove hole" in the floor (I still have one or two in the camping gear room). Usually a zippered semi-circle. They disappeared with the vast rise in tort cases, on which I have no comment, other than to say again that life has risks and I would not care to live in a riskless world.

IMHO it is best to get tell-show-do instruction on using a stove in a tent - from an experienced, safe, competent person. Or skip the idea. If I base camp with one of our really big "packable" tents (barely - need to use a cart), I will continue to use a propane cat heater in really cold weather. Only when awake, etc. Super cold conditions will never see me in those big tents.

On a really long trip without re-supply, I will probably continue to use a white gasoline fueled stove. On anything up to 5-7 days, I have pretty much converted to a cannister-type stove, only taking white gas on weekend trips when I want to refresh my familiarity with a particular stove. For the next 3-4 years it is very unlikely that I will be in a situation requiring me to cook in the tent. After that <shrug> I intend on doing some serious trekking again, so who knows?