Heh, not a good idea I guess, but where @Angela and I lived before, we had lots of carpet. So that just acted as a dust magnet getting it out of the air.
Current place is wooden floors, and I notice myself sweeping and picking up hairballs constantly.
Having no personal experience with it, I would imagine something spandex like would only act as a filter really, still letting smaller (and more problematic?) dust through. Like a dust sieve.