Not really. It's quite confusing to think about, because we're surrounded by a world of forced aspiration, but basically, the idea is that the more air you get into the engine, the more power you have.
Forced aspiration compresses that air, so you have a more explosive mixture to start with, and you can get more in there.
N/A is all about getting as much airflow as you can. And cold air is more dense then hot air, so the colder the air, the better.
The air filter is there to simply stop crap getting into the engine. If the world was a sterile environment, then you'd have no need for an air filter, and the engine would just suck air in from around itself, or from a hose to get a cold feed. So therefore, the bigger the air filter, the more air can get through it at once, meaning that more air can get to the engine at once.
Although there is probably a point where getting bigger won't do anything.