“Air conditioners” are what we normally call the machines that cool air by getting cold on one side (indoors) and hot on another side (outdoors). The condensed water is just a side effect of a cold surface in a humid environment (any amount of humidity above 0% is a risk of condensation) and is a problem to be dealt with. I would not expect it to trap or filter any particles in the air, though I imagine it happens on small scales.
Are you perhaps asking about some kind of air filter or purifier instead? Those are usually just filter based, perhaps leaving a slight static charge in the air because static electricity makes a good filter mechanism for static-affected particles. Neither they nor air conditioners produce any kinds of side-effect gases, as they run strictly on electricity.
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