Bear in mind, the Romans also didn't have glass windows, thus their buildings were not as air tight as modern construction. I am unable to find any references to CO poisoning, but it is not unlikely that it occurred, especially among the operators that had to fuel the furnace in larger installations.

An interesting aside: the Romans were indeed aware of a number of health issues that came with their technology -- a favorite example is the very complete description of the lung disease that asbestos miners would inevitably contract.

We really don't know for certain. We know they knew the dangers of some fumes from fires, as Vitruvius warns against the use of lead pipes.

For when lead is smelted in casting, the fumes from it settle upon their members, and day after day burn out and take away all the virtues of the blood from their limbs. Hence, water ought by no means to be conducted in lead pipes, if we want to have it wholesome.

Vitruvius, Architecture, XI.VI.8

But the idea of ventilation in Roman writings is rather spotty. They liked the idea of fresh air inside:

[B]y opening the windows you let in the western breezes in a free current, which prevents the place getting oppressive with close and stagnant air.

Pliny, Letters, XXIII

But they probably didn’t realise the breathing hazards of open fires or braziers, or the dangers of hypocaust systems. In bath houses the architect Vitruvius was more concerned with ventilation for temperature aspects:

The Laconicum and other sweating baths must adjoin the tepid room, and their height to the bottom of the curved dome should be equal to their width. Let an aperture be left in the middle of the dome with a bronze disc hanging from it by chains. By raising and lowering it, the temperature of the sweating bath can be regulated.

Vitruvius, Architecture, V.X.5

Architects often thought more of windows as a source of light than fresh air.

And as a general rule, we must arrange so as to leave places for windows on all sides on which a clear view of the sky can be had, for this will make our buildings light. Not only in dining rooms and other rooms for general use are windows very necessary, but also in passages, level or inclined, and on stairs; for people carrying burdens too often meet and run against each other in such places.

Vitruvius, Architecture, VI.VI.6

The main thing they seem to be worried about in regards to indoor fires was soot.

In winter dining rooms, neither paintings on grand subjects nor delicacy of decoration in the cornice work of the vaultings is a serviceable kind of design, because they are spoiled by the smoke from the fire and the constant soot from the lamps.

Vitruvius, Architecture, I.III.4

As for cases of people who died from carbon monoxide poisoning, we really don’t know for sure. However, there is speculation that both Emperor Julian suffered from it temporarily and his successor Emperor Jovian died from it. In 1998 the article ‘The carbon monoxide poisoning of two Byzantine emperors’ was published about this in the Journal of Toxicology.

It's likely that they were aware of the problem, and would have ensured that their bath houses were sufficiently ventilated. Afraid I can't think of any good references from Classical writers off the top of my head, but there might be some mention in either Cato or Vitruvius. The ancients were clever, practical people, so there's no reason to think they would have been oblivious to the dangers of CO poisoning just because they couldn't detect it. Depending on how technical one wants to get, they already had a wave theory of sound, an atomistic theory of matter and light propagation, and an understanding of gravity and of Newton's first law of motion.

One curious fact that suggests an awareness of carbon monoxide poisoning is that many of the portable braziers that were found at Pompeii during its excavation were located in large, open spaces (such as peristyles and atria) that wouldn't have been well served by a small space heater. One hypothesis is that, before they went to bed on the night of the eruption, the residents removed the braziers from their smaller, more enclosed bedchambers in order to prevent CO asphyxiation.

As for the assertion about glass, by the mid- to late 1st century A.D., Roman bath houses even in average-sized towns like Herculaneum and Pompeii were being fitted with large glass windows. The technology was adopted fairly quickly in fact, and the baths at Herculaneum even used double glazing precisely because the Romans understood its thermal advantages. That said, it's also true that buildings in the ancient Mediterranean were not built to be so stringently air-tight as we might expect today, in say, North America or northern Europe.