I keep mine sort of the way you are describing. They have a coop that they sleep in at night - during the day they free-range the entire backyard. I live in suburbia on a fairly small plot. The backyard is probably 30x70 with a strip up each side of the house to the front fence that is another 15x20 or so. Guesstimates only on the sizes. The number in my flock is constantly changing but I am allowed a maximum of 12. The most I've had out there so far is 10. Having that amount of space, no, they have not torn up the yard. I still have grass in all of the same places I did before I got them. I will say that they have dug out dust bathing spots along the wall of the house so that doesn't look too attractive. But they haven't destroyed the grass. However the vegie garden is another matter. There is no way to keep them from enjoying it as much as we do, so we fence off the vegie garden to keep them out. After the first frost in the fall, I open up the gate and let them have at it. They spend the winter tilling and fertilizing the garden for me for Spring planting, at which time I shut it off again. So yes, it is doable. You do leave the hens open to predation when you free-range. A risk you and only you can decide to take, although it is wise to make it an educated decision based on the predators in your area. I have not lost any to the "usual" predators, but depending one what you have in your area, your experience may be different.
Edited by HEChicken - 1/30/11 at 11:12am
I will say, lawns have never mattered that much to me. I don't see grass as being particularly useful, so can't see spending a fortune on fertilizer and watering, to maintain it. I used to have clover in my backyard but I guess the chooks really enjoyed it because there isn't any left. I am considering overseeding this Spring with some other grains - clover, perhaps some brome, maybe some millet. It will be an experiment to find out what they like. Anything will be more nutritious than the fescue, I'm sure. However to ensure it gets started without them eating the new shoots, I'm going to fence off a small area, start the seeds, and once they are established, take the temporary fence down and see how they like it.
Editing to add a photo taken in early August. This is mid-summer of the second full year of keeping chickens in this yard. In the photo, my husband is sitting in a chair against the back wall of the yard and you can see the retaining wall and deck posts, so you can see how close the house is (to give you an idea of yard size). You can also see how much grass there is - and this is with them on it from dawn to dusk every day.