Goats and Deer have similar digestive tracts. They both have a single stomach that has four compartments just like a cow. And they al eat food and belch it up so to speak and chew it up again--It is called chewing their cuds and it is part of the normal digestive process that they all share. And...
Yes your chickens will peck at hedge apples and it doesn't hurt them. Mine do. I put them in the chicken house to help keep bugs out and WELL the chickens like them also--And yes deer and goats do eat them also, Our cows have been eating them but they can choke on them if they don't crush them...