It's unknown if lack of sleep causes the onset of Alzheimer's, but the opposite is likely true: Alzheimer's patients don't sleep well. So once it starts to develop, it spirals down likely because of sleep deficiency, thus accelerating memory loss.
Source: "Why We Sleep", by Matthew Walker. We had a few threads recently about the book here [1], [2].
The link is alarming enough you should think seriously before taking things like Zzzquil, Benadryl, Tylenol PM, etc. if you value your mental faculties.. But maybe the correlation in this article is at least partially explained by this other link. Personally the other theories (brain garbage collection during sleep, etc.) also make a lot of sense. And don't forget about the fungal theory: https://www.ncbi.nlm.nih.gov/pubmed/24614898