question about sealed room co2

hi this is my first time post here , just had a couple questions now that I've switched over to 12 gavita LEDs

I want to implement co2 but had couple questions the way my room is set up right now is air in and air out with a 10 inch carbon filter at the top of the grow to exhaust out. now if I sealed my room would the co2 escape thru the carbon filter when it's turned off ? co2 is heavier so it should fall down correct?

the walls are lined with panda but we have regular doors to go to each room how do you guys seal the doors to prevent leaks?

or can I simply add co2 , close off the air coming in, and turn on the exhaust out (carbon filter) when the plants are sleeping. I have a 6 ton ac unit so not worried about the heat. thank you