After an animal dies, any wounds can't fester. Natural decomposition sets in. But, since you were butchering the hen within 5 minutes, she certainly wasn't even decomposing yet. There is nothing wrong with deciding to eat her. I am a whole lot more squeamish about feathers on the table than I am about your family eating her.
I was amazed by the yellow globs of fat on her...we give our flock scratch during the cold winter months, I assume that accounts for part of it. 