How efficiently are the aerosols and droplets sucked into the AC system? The principal method of spread is by these vehicles, person-to-person, at close range. Imagine a church with most pews filled. If the AC provided absolutely pure air (forget for the moment about how this is created), it would do little to prevent virus spread between unprotected individuals.
You could, in theory, build a system like what they use in datacenters. Drill holes in the floor and ceiling and create enough vertical airflow that any particles you expel will be sucked either up or down before they reach the next person.
That would make a very uncomfortable church to sit in, though.
I'm basically taking this from an earlier hn discussion about the lack of a documented early outbreak in Las Vegas: apparently the casinos have systems powerful enough (and surely involving clever placing of inlets and outlets to enforce a coherent vertical stream) to allow indoor smoking without driving away non-smoking customers. This has since become my mental model of what it would take to make an indoor environment as safe(ish) in the pandemic as the outdoors.
The indoor air quality at casinos with smoking is better than a bar with smoking, and it's not enough to drive me away from walking through the casino to get to the hotel, but your clothes still smell like smoke when you get to your room.
I would put it as tolerable, maybe if I enjoyed gambling or drinking, I'd be ok with being on the casino floor for longer. Better to go to the enlightened casinos with no smoking though.
For my mental model, I usually think of underground mine ventilation. Requirements are typically in the range of several cubic metres per minute per person - enough ventilation to be able to feel a light breeze.