The effect being refered to here is that CO2 comes in cans or ice, and thus is super cold when introduced to the normal pressure air, this is because evaporation causes cooling, eg when you come out of a lake and the wind hits you and you get told to stop pointing. Now, would it be enough, and would you want it if it were. I think its possible, if you had enough ice or liquid, sure i think you could do it. But now, would you want to. First, there's price, that would cost a lot of money to have that kinda co2 being evaporated into the room, and the room would have to be pretty well ventilated to keep the evaporation, and thus cooling, in operation. This would be a big waste of CO2 and could result in security issues if the ventilated air is not dealt with properly. Second, you could probably achieve a better ammount of CO2 in the room by having it well sealed, but then the cooling wouldn't work.

My suggestion, don't use the CO2 for cooling, that's really expensive, use independently vented lamps so that the air can be drawn from outside the room across the lights and out again without ever picking up the smell of the plants. Also, this method would need CO2 from a bottle or ice, no generator would cool anything, it would heat it up big time, it is a flame after all.
In addition, if you had cold air, say from an airconditioner or the outside in winter for nothern regions, then you could not only take heat from the lamps, but also take heat from the air in the room as transfered through the metal, glass and plastic of the vetilation system. Some modification may need to be made , eg fins on the outside of the metalducting.