When I moved to my house, the property had a coop and covered run area that was completely devoid of life. I've been here nearly a year, and just a few weeds in the place where the run used to be; I'm thinking that the chickens must have eaten every last little weed/grass seed there was. My neighbors tell me that the original owner used to give away eggs galore, so I'm thinking the hens didn't mind the bare ground. The neighbors also said they traded food scraps for eggs, so I'm thinking the chickens must have gotten supplemental McFeed...
The one thing I noticed is that the run area is more gravelly and sandy than the surrounding soil, so it looks like the owners amended things a little. The soil drains MUCH more quickly than the surrounding soil, and stays a lot drier.