There is a statistical link between periodontal disease (gum infections) and clogged-up coronary arteries. It adds up to about a twofold risk for heart disease. You can google something like" coronary artery disease and periodontal disease" to read the recent studies, if you're interested.
No one knows yet exactly what is going on, or whether it's really cause and effect. Myself, I'd minimize my risk with flossing and gum care, for they're not expensive and take just a few minutes out of the day.
From the internet: "The evidence isn't clear yet, experts say, but it's intriguing. According to the American Academy of Periodontology, people with periodontal disease are almost twice as likely to have coronary artery disease (also called heart disease). And one study found that the presence of common problems in the mouth, including gum disease (gingivitis), cavities, and missing teeth, were as good at predicting heart disease as cholesterol levels." But you are implying that all old people have teeth/gum problems which is absolutely not true e.g. I am 78 years old and still have all of my teeth albeit with a few fillings.
I'm not sure it actually causes heart disease, but it can certainly attack smooth muscle, such as the heart and valves. The thing is, it's rare and so it won't affect everyone.