Corn is a carbohydrate that provides heat energy that you would ideally give in cold weather. I know that the pigeon feed I use during winter includes corn. Pigeon feed that peeps use for racing does not contain corn.( I don't race.) The corn is the last thing that my pigeons eat... It is also the last thing left when I give my chickens scratch or other grain combinations. Being totally sincere. I don't think corn is going to hurt chickens or pigeons . It will not overheat them. They will only eat as much as they need. They will have energy to burn in activity. Nutrition is of course complex. Proteins are body builders. Fats are also needed. Corn is labeled as a good feed but not to be used exclusively. I have read the labels on cracked corn bags . Consider it as a filler food. It is also the least priced grain. You will see that unless your chickens are very hungry, they will not be gobbling up that corn quick.
WISHING YOU BEST.
AND YES