Yes periodontal disease can kill your dog if the periodontal disease is left untreated and progresses.
Eventually as the periodontal disease progresses further and further the periodontal disease in the dog can infect the dogs blood.
Then when the dogs blood gets infected from the untreated periodontal disease organ damage can occur in the dog which can then lead to a heart attack, heart disease etc in the dog.
The dog doesn't die of the periodontal disease itself but instead overtime as the periodontal disease in the dog progresses it causes heart conditions which can then lead to the dog having a heart attack and dying.
So if you can have the dogs periodontal disease treated by the vet.
However if the dog is older and is about to die anyway within a few years or so then it may not be worth it to treat the periodontal disease in the dog.