Actually can. Air - conditioner also can, but the filter of the air conditioner is little bit bad, as the hole is too big, but can filter big bust. Air purifier can filter small dust, but not all. If you think the dust is on the surface of the furniture and you are not satisfied with it, use a vaccum cleaner to clean it.
Actually, the dust will not affect you, and it will come after few hours you clean it.