This is a weird question, but it's bugging me so here we go.
Even if animals had vocal cords comparable to those of humans, would they sound human? Not only are their throats shaped differently, but their mouths are too. For starters, the mouths of most mammals are open on three sides (dogs, cats, mice, etc.) rather than on just one side like humans. Also, they have longer mouths and their tongues work differently. They surely don't have all the necessary muscles in their lips/face. So maybe a better question is: Would it be possible for animals to have all the necessary elements to produce human-like speech while still maintaining the same appearance they currently have? If not, how close could they get?