It absolutely does in my opinion. Just talking deer, I've shot them with a 375 H&H down to a 250 Savage and nothing kills them faster than a 257 Weatherby with 100 grain Hornadys at factory specs. I've never had one take a step when shot with one and I try to shoot all my deer on the shoulder.
Randy Brooks told me personally years ago the 416 seemed to kill better with the 350gr TSX than with the 400 when he was testing them and he could only surmise it was the difference in velocity. Lastly, Ross Seyfried in his book tells where the most impressive buffalo killer he's ever used was the 416 Weatherby @2700 fps.
A stoutly constructed bullet that expands and penetrates well will add a lot more internal trauma when driven faster, no doubt.
