Haha, I'm writing the introduction to my thesis, and I thought that this part might be an interesting general topic. Your question is related to a topic that I've been thinking about doing a post about. Typically, cognitive aging is broken up into "normal" aging and "disease-related" aging. Normal cognitive aging can occur in the absence of disease, and the diseases have typical biomarkers and trajectories that differentiate them from normal cognitive aging. I'm talking only about normal cognitive aging above. So to answer your question, no, cognitive aging does not seem to be the cause of dementia and Alzheimer's.

However, some researchers have started calling "normal aging", "healthy aging", which seems like a misnomer to me. In my opinion, if someone is suffering from any cognitive decline that is related to some biological root, then that is unhealthy. I know that they're just words, so it might sound pedantic, but it's important. Aubrey de Grey has discussed the "pro-aging trance", which is the tendency to justify some normal aging processes as unavoidable, natural, and maybe even desirable. I think that if we started regarding normal age-related cognitive decline as a disease, too, (although not a terribly devastating one), we might make more progress towards its ultimate prevention.

Since dementia and Alzheimer's are usually age-related diseases, it makes logical sense to me that some of the root causes of normal cognitive aging and the diseases overlap: unhealthy vasculature, cellular damage, inefficient metabolism, weakening immune system, etc. So I do think that there is a connection between the two, even though they are separate things.