I think it's best to periodically brush your dogs teeth with a finger brush (like you'd use on babies)using a veterinary toothpaste (swallowable).
Some dogs are more apt to get tartar deposits on their teeth than other dogs. Why? Because of the chemistry inside of their mouth. The breed doesn't matter, it's the individual dog that does. You could have two say labs, feed them the same food and one may develop tartar while the other doesn't.
So if you have a dog with tartar a rinse may help change the chemistry in the mouth and prevent tartar build up. I don't think it will remove any existing deposits, but may very well prevent new ones.
As far as having an old dogs teeth cleaned you can lessen the risk significantly by having a basic metabolic panel run on the dog before using anesthesia. This will show anything that may be wrong with the dog that may cause the dog to be a risk for anesthesia. Our lab/golden Brandy just had her teeth cleaned and now they are nice and white and sparkling, and she's 13 years old. But she's not really overweight and all her tests came back just fine. But I think that's the last time she'll get them done. Usually it's about every three years.
And check around for price. My vet charges $250.00 for a complete cleaning. I have heard of people paying $500-850 for a teeth cleaning before.