more then likely you'll hear it more.
but if you take the cover off then you are defeating the purpose of it. its made to keep the hot air out of the intake, so its still drawing through that 4 inch hole on the side of it, where its getting much cooler air vs whats under the hood.
if your stock having that box dont really add up to much. no hp to be gained, just looks cool. you could maybe send it back and make your own intake for about 40 bucks. its what most of us do. and you can hear it whine like mad.
where in NJ are ya?
