Much of the flavor in soup comes from the meat cooking in the broth. I wonder if it would not be as flavorful.
The best chicken soup I have had is made as acs suggested. The soup was made with an old chicken that was used for flavor. Once everything was done the meat and carcass were discarded and uncooked chicken was thrown in the pot and the soup served. No need to precook the chicken though as it cooks in the soup very quickly.