Assuming there is enough smoke to trigger them which IMHO is not very likely.
Trouble is CO is a rather insidious toxin, nice and comfy and warm in your chair, relatively low level CO helps you nod off and you stay nodded off...
The CO alarm we have has several warning states, flashing LED, flashing LED and a short beep, LED and more beeps and finally full alarm. The level and duration of the CO determine what it does. It goes into the first of those at CO levels over 43 ppm. 35 ppm is the maximum continuous 8 hr exposure level.