Purifier?...those gimmick things sold by Brookstone? No.
Air exchanger? What is that?...what do you mean?
Active cross ventilation, using adequate supply outside air, while drawing it in, to a discharge fan, will reduce buildup ( of anything) in the indoor air. Mixing is also a factor.
It will also cost you a lot of $ in heat or air conditioning, if applicable. In short, generally impractical
This post is specific to a church considering return to in-person services. Social distancing commitments include enforcing six foot seating distancing from unrelated worshipers, non-contact, non-touch practices, mandatory face covering, and continuing live streaming for vulnerable risk groups, While the committee is working hard to identify and mitigate risks as much as possible while allowing resumption of services within the church facility, there is still concern. There are three outside doors that can be kept open which would provide some cross ventilation into what is a sanctuary in the round. there is a ceiling/attic fixed air exchanger above the sanctuary. Not sure if that would help or hurt?
I would say that with passive ventilation as you described, and depending on space size, layout, etc. you have to assume a low level of dispersion/dilution at any given location. But, your use of other mandated practices, does make this less risky. (I was assuming non masked in a home type indoor setting)
Any thought to checking temperatures of entrants?
Its just a matter of improving the risk profile of the situation. There is no magic, "it's safe" if you do x, y, z.