Filled one of my black bear tags a couple years ago with a BRS-99 (9mm carbine). I was testing it, had it on hand, and had a bear tag when we had a troublesome bear. Figured why not, it worked with a 147gr Gold Dot from ten yards in the vitals... Or was it a Hydrashok, or SXT...? Can't remember but I'll look for a pic I took of the recovered bullet from under the skin of the far side.
This said worked as even a .22 Magnum likely would have if legal from that range, with that placement. I wasn't impressed by any measure, it looked like an arrowed animal, ran for nowhere at Mach 1 and died running about a hundred yards into the bush. A lot less blood trail than an arrowed animal, meaning none, lots of blood in the chest cavity. My rationale in trying it was the 147gr 9mm is equal or superior to a .45 round ball traditional muzzleloader, and I've taken that afield (though never shot at game). If you can get inside archery ranges, place shots perfectly, and use a heavy, quality HP yea it kills which isn't a big surprise.
This said, you're putting an awful short leash on your hunting, it would quite literally be my utter last choice. I bold that because I don't want this post cherry picked for the crowd that picks info they like.. If you happen to find yourself in the situation, and are willing to sneak up stupid close, and have no qualms turning down the shot if the angle changes- why not. But also, why bother? For me it was the only gun I had, we had a nuisance bear, I was curious, and I had a tag to fill. My curiousity is fulfilled and I'm done with pistol chambering carbines below .45 Colt.