Is activated charcoal an air purifier?
Agreed: unless air is pushed through the activated charcoal bed, few impurities would be adsorbed. 
It would depend on how tightly the substance clings to the carbon, i.e. it would vary with impurity, but Trox Technik KS Filters recommends, "saturated activated carbon is reprocessed... with a gradual increase of temperature from 20 to 830 °C and a delay period of approximately 30 minutes."
Finally, how long does the air-stream remain in contact with the filter? It would seem that most air bypasses the pores of the carbon on inexpensive commercial air filters. Activated charcoal might be of more use in reducing foul odors in a closed container, such as bottles of medicines.