It seems that the "cover" is harder than the other parts...
It would be edible (for true Parmesano Reggiano, anyway), but it may not be very pleasant, as it is where most salt from the brining period will be, and it is dry and hard.
It is traditional to use pieces of it in soup to add flavor to the broth.
Someone mentioned adding to soups and stocks...I also save them for that purpose. However, a family favorite, is to insert, with other aromatics, in the cavity of a chicken that will be roasted. Remove when carving and serve with the chicken. It will be soft and delicious.
Absolutely edible, specifically goes well in hot dishes like soup.