The Webley tri-pump I have sucks air in through one side of the tee-bar handle via a sintered metal filter and a pack of silica gel. Standing the pump in a bag would not be detrimental to the pump or pistol, but I can't see it making any difference...
As for the pump, I bought it for £50 from a mate as it had stopped working, I fixed it by replacing the tiny, tiny 'O' ring at the very centre of the pump. That has lasted two years, so I have stripped it down again, new seal with some cleaning and lubing, and hope it will be good for another good stretch.
Tanks are scary...
Too many guns, or not enough time?