They do, but not for the reason you're thinking. When their teeth wear down to much or get broken they can't get them fixed. If they can't eat enough food to maintain their health they will die. On the flip side sugar is relatively rare in nature, so they don't get cavities like we do. They can get them, but not like we would with our diets and no dental care. Pets that eat human food often have cavities just like us, not to mention all the other health problems that can cause.