It depends what kind of plants. Many people are allergic to pollen.
Plants also need maintenance, if you let it overgrow - or let it die - all sort of bugs live on the soil.
There was a slight volcanic smog last week, and the plants certainly did not help.
We have 1 air purifier, a cheap one, I placed it in the room of the children. Thankfully the sulfur dioxide in the air has subsided.