These broilers are a result of crossbreeding two different chickens, the Cornish and Plymouth rocks. This results in somthing called hybrid vigor, where the offspring get the best traits from either side, and grow much more vigorously then either parent. If you were to breed males to females, you probably wouldn't get chickens quite like your broiler stock, as well as they wouldn't grow the same.
Also, sometimes larger chickens have fertility issues, and I suspect that these would need some help breeding, much like the BBB turkeys.
Even when they aren't butchered Cornish Xs seldom make it to sexual maturity, usually dieing of heart failure and other fast growth causes. If they do make it to sexual maturity, they can't breed naturally, they need to be artificially insemenated.
Any chicken that is a hybrid is a mutt, though a mutt with good traits. You don't know exactly what you'll get with breeding them to each other or other birds, except with trial and error. Any of the heavy hybrids made specifically for meat consumption aren't made for longevity or egg laying, and I would expect them to just eat and eat until they get so fat they die.
Perhaps you want to look into an actual breed of chicken, if breeding your own stock is what you really want. Or, you could buy the parent stock for making your own Cornish Crosses.
darn i was hoping that i could get a type of meat bird that could breed with regualar hens to create some kind of my homemade way to make a good laying/ meat bird i know meyer sells their extra males for meat birds... i will email j and m i think that is the place to see how they do it lol Thankyou