Will you be putting a drop of the cleaning oil on the filter, Dan? At first impression I'm inclined not to, and for this reason: even that light cleaning oil will just collect more dirt on the filter, and in the end make the condition worse, and you'll be engaged upon an endless cycle of putting drops of oil through vertical sprocket holes. I don't think the pedals turning is enough of a nuisance to turn it into an everlasting worse nuisance.
Or, more succinctly, It's against my ethos of a minimum maintenance bike, thank you very much.