There are two kinds of meat birds. The cornish cross birds that grow an incrediabe rate, and are ususally ready to harvest between 8-10 weeks. They eat a lot of food, and produce a great deal of poop and must be harvested on schedule or you will lose them.
Then there are the pioneer birds, and red ranger birds. These grow a bit more slowly, and the harvest schedule is not so tight, but will still produce a nice carcass at about 12 + weeks.
I have been thinking about trying what you are proposinng, and I think I would go with the pioneer or red ranger birds. However, the above poster HAS done this, where as I am still in the theory stage.
Mrs K
This is a great point of discussion.
In my experience, Cornish Cross will work better for frequent rotation. This is because other chickens seem to think of Cornish Cross differently - I wouldn't be surprised if in their little chicken brains, they thought of them as another species. This has to do with their behavior, mostly. They are content to sit and eat for hours on end. Because they are mostly sitting in the same place, occasionally waddling to the waterer and back, the hens don't find them interesting or antagonizing. If you watch bullying in a flock, you will notice it escalates quite quickly - a chicken is picked on, it gets nervous and tries to run, which results in the picker getting more aggressive, and the picked on bird running MORE frantically, so on and so forth. Cornish, when picked at, will flop a few feet away and sit down again. They aren't active at all. However a Ranger/Pioneer is going to act a LOT more like a normal chicken - running, screeching, doing all the pitiful things a regular picked-out bird is prone to do.
It would also work better because Cornish grow larger, faster. You can put Cornish Cross outside at 3 weeks, no problem. 4 if the hens are brats. A Ranger/Pioneer of the same age will be quite a bit smaller, since the weight they put on tends to be at a later age.
This isn't to say Rangers/Pioneers WOULDN'T work. I expect there would be more picking and aggression, but with proper management, it's definitely still feasible - my original Rangers were raised as part of my big yearly crop, and did well, despite the higher amount of picking. The Cornish Cross are simply easier, is all, and that's why I use them as the main fowl for my big yearly crop and smaller rotations through the year as well.