The nature article is a fascinating read [1]. Not only is there a health risk, but there seems to be strong evidence that it effects our cognitive abilities. This should be top priority for office workers, and managers to maintain high productivity. Start monitoring CO2 level such that they do not go beyond 700 for too long. Currently, I'm working on in an office with 13 people in little over 20m2. Yeah, we are scrappy, but I think this might the reason that we are all so tired at the end of the day. CO2 levels might be out of control.
Conveniently not mentioned is this article is the fact that normal CO2 concentrations in human lungs are about 40,000ppm - or about 100x higher than current background levels, and many times higher than the elevated levels mentioned in this article. And I don't know about you, but when I'm in a crowded room what eventually makes me tired and uncomfortable is the heat and humidity from all those bodies. Turn on the AC (which reduces both heat and humidity) and I will be feeling much better in short order.
It would depend on the situation. For a single room system, generally no; for a multi-room system, generally yes if the other rooms are empty or at least relatively less crowded than the one you're in. That is, I wouldn't expect the AC to really remove any CO2; it might redistribute it, though.
Heat dumping is done outside the room, of course, but that's a separate airflow, one that's generally disconnected from the room. The cool AC flow itself is usually a closed cycle of some sort. You would be kind of defeating the whole purpose of trying to cool and dehumidify the air if you did otherwise, plus your AC system might have to run continuously in order to get anything done. There will always be some leakage, of course.
When constructing a home office, I tried to calculate the ventilation-airflow requirements to keep the office CO2 below problematic levels. IIRC, I assumed two persons occupying a 1200 ft^3 space, with replacement air coming from the rest of my house.
I'm not sure my math was correct, but the required airflow rate was surprisingly high, maybe in the ballpark of 100 cfm? Well above the ASHRAE 62-89 recommendation of >= 20 cfm/person.
[1] https://www.nature.com/articles/s41893-019-0323-1