Yes a dog can die from a tooth infection that is left untreated.
If the tooth infection in the dog is not treated the tooth infection leads to the blood getting bacteria in it and when the blood gets bacteria in it the dog can have a heart attack and die.
So if you have a dog with a tooth infection it needs to be treated if possible to prevent the dog from becoming sick.
I had a dog that had a tooth infection and I didn't think anything of it and though it would go away but then a few months later the dog died.
I asked a vet and he said that the tooth infection is what likely killed him because the tooth infection infects the blood with bacteria that then causes heart disease and heart attacks in dogs.
A tooth infection can also get severe enough in humans if left untreated and lead to death.