Could be. Hawks around here will sit with their prey and pull feathers out..... But don't you think that even a hawk would try to carry off it's prey...as long as the prey wasn't bigger than they are.
The largest chicken hawk in North America is the red tailed hawk. They grow up to about 4 lbs. Therefore I doubt that any hawk is capable of toting off a standard size, adult hen or rooster. The only way it is possible is if the hawk eats most of the chicken while it is still on the ground then flies away with the scraps.