> Do goats eat and poop 24/7 if left unchecked
Yes. Many grazing animals are like this. It's like they have no "feeling full" in their tiny brains. Grass and leafs are not very calorie dense so they kind of have to.
Cows or horses can easily eat themselves sick if they are let into high grown grass fields. Where I live the horse owners will sometimes cut the grass in the fields before they let the horses go to it in the spring.