It would! Back home, people can summon various animals to fight alongside with them. They're known as summons. You basically find an animal, and make a summoning contract with them with your blood. I'm not sure what the difference between creatures and natural monsters are, so I can't really address that part, but you are right about the summoning thing from another world. I'm sort of wondering how the system came about as well... [ Considering, considering... So many things to consider! ]