I think you're fine. Step 1 in evisceration, after removing head and feet is to remove and loosen the crop and esophagus so you get a clean pull through, at least that's how I do it. If he's processing professionally, it's highly likely he's inspected at least at the state level, so it's pretty safe to assume proper cooling protocols.
Hens go broody when you don’t want them to… and won’t go broody when you do. 
