It could be fun - and if the "hunt" monsters roam freely and are aggressive, might add a little bit of much-needed danger to wandering around in the wild. Give them a long leash and a greater chance of Weight, so they can be properly terrifying! :3

I would suggest, though, that such monsters be given a significant defense boost if you're not currently assigned to hunt them, so that wandering parties don't kill them for the lulz and spoil the hunt for folks who are actually hunting.