I think it could, provided the user is as good a shot on both still and running game as a bolt, lever, or pump hunter. That doesn't mean that the average "Gravel Pit Master" can fully take advantage of the firepower afforded by a semi-auto. Why? I think that many semi-auto hunters tend to shoot the first shot before they are on-target for a quick kill, especially on running game! Each shot after the first one is usually a worse situation than that first shot, so that first opportunity should be delayed until the sight picture is as good as it will probably get.
The first deer I ever shot was running across a big field, after being shot-at by another hunter. I took my rifle out of the car, loaded one round, then leaned on an object and fired as it topped a ridge in a hayfield, 200 yards away. It went down dead. That was about 55 years ago, when in my early 20s.
Since then, I've killed several running deer, and yes, missed a few, but rarely wounded any to have them escape to die a horrible death. A few times, I've mentioned my favorite, shot left-handed from a tree stand, but all of them that I hit were done with a bolt-action. I've missed with handguns and a shotgun with slugs and think that a bolt-action might have gotten those critters because I'd have been more deliberate because I may have had only one decent opportunity, and would have used greater care.
JP