Filtering the air going into an inflatable mattress, chair, pool toy, etc is a mindless exercise. There is no purpose in it. It has no effect on the inflatable item if the air is dirty.
Just walking around downtown in any city in the summertime is going to have 20x more dirty air than a vacuum cleaner.
Also just FYI the air inside an air compressor is full of rust and motor oil as well as mildew from condensation from expansion and contraction of the air. That's why they have drain tubes.
An old air compressor that was not cared for and exploded: http://uploads.tapatalk-cdn.com/20160317/f5043f769cc1f88e747d227d9ac67762.jpg
