No expert here, just my opinions.
As far as OČ and CO, I don't think having the cover on would be much different than being inside with the door, windows, and rooftop vents shut. Thinking the cover would have to be on tight to cause a problem there. .
But, you'd probably have more condensation inside since you couldn't open a vent. This is something you don't want too much of.
Again, these are my thoughts. I might be way off base!