What constitutes much noise is subjective, I suppose, but any fan moving hundreds of cfm will be very loud. A 140mm fan moving 20 to 30 cfm is still audible, if you're in a quiet room.
A common approach is to have an intake filter that catches dust. Another is to elevate the case a few inches above the ground.
Both of my recent hardware failures have been caused by dust accumulating in heatsinks, so having something which contributes to that is also a "very bad idea". Especially since the air passes through a relatively confined space which you can't regularly clear out.