techbsmith
Chicken Hoarder
Not if it's installed so it's flat to the ground, and the grass is allowed to grow back up thru it....then it becomes nearly invisible and the animal will start digging where the wall meets the ground.
Sometimes you need to mow the grass really short, or even take up the sod, and use some landscape staples to get the mesh to lay flat so the edge is not visible to a digging animal, or becomes a tripping hazard for humans.
I cut/removed the sod around my run, laid the apron down on the ground and covered back with the sod I pulled up. After a few weeks, I couldn't even tell I'd disturbed the sod and the apron is well hidden.
I used hardware cloth and some concrete reinforcement mesh I had left over as the apron - so there's actually two layers with the hardware mesh on top. It runs down from the walls of the run, bends at 90 degrees and goes out 2' from the side of the run.
We've got some prolific diggers where I live, so I may have went a bit overboard

By the way - the pic of your EE just about made me cry. She's beautiful and reminds me of my sweet girl.