In my basement, the ceiling of one of the closets is the copper grounding wire that runs from the breaker box to my water main. This wraps around the perimeter of the basement on the top of the rooms and I'm installing a cloth ceiling for acoustic purposes in a closet to record in. I put acoustic insulation between the joists and then just stapling muslin as the covering material.
The cloth is touching the wire in a few spots, and I didn't know if that mattered at all. It's not live and can be touched, but In my nonexistent electrical knowledge, I didn't know if current ever went through that wire. Take a look at the picture and you can see what I'm referring to. 
Best Answer
If your wiring is right, the ground does not normally conduct current, so it should be fine. (The bare ground runs along paper inside romex after all.)