Yes, CO is similar to air's molar mass (it's actually slightly lower), meaning it will diffuse evenly through the vertical space in the room. The concentrations at the ceiling will be the same as the concentrations on the floor.
Stop spreading misinformation.
Diffusion of gasses in the air is an extremely rapid process. In a minute the concentration would be the same throughout the room.
"Should the placement of carbon monoxide (CO) detectors be influenced by CO's weight relative to air?"
http://neilhampson.com/uploads/3/4/0/6/3406995/2011co_weight....
Their conclusion agrees with you completely:
What does this say about the placement of residential CO monitors? It would be reasonable to place them anywhere in the room and expect them to be effective. Every scenario imaginable in a home would only speed the mixing of the gas within a real room, as compared to a sealed chamber — people walking, forced air flowing from vents, CO entrainment with warm air being released into a room at floor level and then rising.
The belief held by many that CO sinks is clearly wrong. Statements such as ‘‘Carbon monoxide is heavier than air, and will pool in lower areas’’ need to be refuted with facts (5). Even if CO were significantly heavier or lighter than air, it would still distribute equally from ceiling to floor.
On the other hand, they did find that the rate of diffusion can be much slower than "in a minute":
The time required for the equilibration of CO concentration was different depending on the level of infusion. It occurred most rapidly when CO was introduced in the middle of the chamber (2 min), at an intermediate rate when introduced at the bottom (40 min), and most slowly when introduced at the top (105 min). Nonetheless, the ultimate concentration was equal throughout the chamber, with no suggestion of any pooling on the floor, layering in the middle, or floating on top.