Basically the mesh would only be to keep the sides of the tunnel secured together to keep from rattling around. You'll need to cut the bottom of the tunnel out (side closest to the mobo), I'd try just running it like that first and see if there's any unwanted rattling or noise. If there's not, you don't even need to trouble yourself with the mesh.
However, if the metal vibrates a lot, then you'll have to look at a way to keep it from moving. I'm not too sure how much a wire grid will help though; how have you attached the wind tunnel to the clear fan casing?