A few hunters in an area with a decent number of animals can keep a fortress going for a few years actualy, the problem is that, in order to support a fortress, not only do you also need a dedicated butcher and tanner if you don't want to waste anything, but they also need to kill faster then wildlife spawns in order to support your fortress, and you need to remember to make bone/wooden bolts once in a while or they'll end up hammering their targets with the crossbow.
Pluses: Hunting usualy brings alot of different meats so your dwarves will probably never get tired of eating those meals, most animals generate 5 pieces of meat and fat, and will provide you with a good, steady source of bones. It also goes very well with tanning, so if you want leather goods or some leather armor, they're your dwarves, plus they'll become legendary marksdwarves in a few years, depending on what they're hunting, and if they survive that long.
Its also nice to have a legendary hunter outside during sieges, at certain times, i had one wipe out half of the siege party on his own.
Cons: They tend to get overwhelmed by the wildlife at first, but getting them some hunting dogs for the first months will make them considerably more durable. They tend to get caught in ambushes often, and getting caught in the crossfire during sieges. You mostly need to train their marksdwarf skill for a bit before sending them out, preferably with some expendable armor, and they also need quivers.
Also, once your wildlife has all been killed, they'll be useless for a loooong time unless you draft them, but then they'll become champions really fast and you won't be able to undraft them when wildlife respawns.