Can I die from periodontal disease?

Increased risk. We know that severe periodontal disease increases risk for certain conditions - like a heart attack or a stroke, however, these are multifactorial conditions. It will not cause a heart attack just increases risk along with other risk factors. The bacteria that cause periodontal disease can get into the blood stream and thus affect other parts of the body.
Oral-systemic link. The prior answers are very thorough. It is very important that you address these problems asap. Latest info shows a link between many medical conditions and periodontal disease. You may lose teeth and your oral hygiene will have to be the best to have improvement. See your dentist for a thorough evaluation.
Unlikely. Very unlikely to die from periodontal disease if it is appropriately treated. Rare instances, in case you have certain underlying heart disease or immunosuppressed conditions, you may develop an overwhelming infection.