I was under the impression that pushing is less efficent due to two things.
Foil pipes usually have small holes so smelly air seeps out of these.
Secondily, pulling is more efficent because it sucks air through the gaps in the air filter like a vaccum, where as if you blow, most of the air hits dead ends and is relying on more and more pressure to force it out.
The radiator in a car is a perfect example. Pulling air through it with your mouth is easy from 1cm away. Blowing air through it is like a brick wall. Thats why fans on cars pull rather than push.
As for the Cover sleeve, defintely use it if pulling air. It collects huge amounts of dust that would block holes in the carbon. If your pushing, you'd almost want a filter on the inside if thats possible (i've never seen it)