Like WOL, I wouldn't do it, any frankly wouldn't do under any circumstances with any weapon. I take that mesh off *all* of the windows the minute I get a new ground blind. As a guy who has seen bullets and arrows deflect off of the slightest twig in the field, I want absolutely nothing contacting the projectile on the way toward the target.
Moreover, I have seen zero loss in effectiveness using a blind without mesh and simply open holes in it when hunting deer or turkey. I have heard old wives tales about "black hole effect" and the large openings spooking deer, but I can assure you that it's bunk. Hunters frequently mistake deer spooking at the sight of a blind in their comfort space with the idea that it's the unmeshed holes somehow spooking the deer, or that the deer can make them out inside of the blind when they are sitting in it with open holes.
What will spook a deer is a freshly setup ground blind appearing overnight in a frequently travel location. Deer don't take well to big, new furniture. Taking down and setting up a pop-up blind repeatedly in different places without letting it sit for a while will surely scare a good number away. Leave that same blind there for a few weeks and the deer will stop caring, mesh or no mesh, with you sitting inside of it, even moving around in it within sensible limits. I've had deer nearly put their head inside of a blind I was sitting during turkey season because it sat in the same meadow all through deer season - no mesh over the windows.
Bottom line: ditch the mesh and ditch the risk of a shanked shot. You'll be fine without it.