We have 4 cornish cross birds out in our chicken coop--3 hens and a rooster. They're about 4 months old, they forage, they scratch, they have good, strong legs, they're active, they're normal chickens. There was a point while they were in the brooder that I was worried about them, they just laid by the food and barely moved. They grow so fast you have to monitor their food intake and cut back accordingly. As soon as we let them out with the rest of our birds and all the food they got was what we threw on the coop floor, though, they just took right off and they're very happy and healthy.
You can raise cornish cross without harming them. You can pasture them, if our 4 are anything to go by they're great foragers when that's all they get to eat lol. They love grass clippings and kitchen leftovers just as much as any other bird.
Because of the muscle mass they are genetically predisposed to have, though, they will ALWAYS need more food than your layers. This goes with any meat breed, but the Cornish X is like the frankenchicken of the meat birds. They're grotesquely large in comparison, and even once mature it's my understanding that they just want to eat, eat, eat. Unless you plan on trying to breed some of that into a more stable, slower-growing and less dramatically muscular bloodline, be prepared to have the processed or meet their feed requirements. Also, they're bred and "designed" for low-grade corn and soy based foods. Super efficient on that stuff, but higher quality stuff or even pasture? Efficiency might change dramatically.
But our 4 cornish x are doing quite well, they're happy, but they don't have free unrestricted access to a feeder and have had to work (scratching and walking around) because we scatter their daily food supply all over the ground of a very large chicken run. I've heard of other people keeping a hen or rooster well past maturity for whatever reason and they do fine. A Cornish that's going to be sickly or have leg problems probably will show signs of it by 10 weeks, in my not so expert opinion. Ours keep up with our ducks, barred rocks, and new hampshires for the most part, but again, their freakish bulk does come with a catch. Most of them can't get up high enough to roost, and I don't think I want them to because I'm afraid they'll snap their legs or something when they jump down.
I'm of mixed feelings, I'm generally in the "it's more humane to kill them now" camp but I also know of people who have kept them well past maturity as layers or pets. But they eat a lot, they never stop being hungry.