I tell patients to follow the evidence when it comes to herbs and spices and alternative stuff - all medicine for that matter. Direct evidence - randomized clinical trials/large population studies over time, not the tangential stuff like antioxidants are good for you, evidence shows wood pulp suppositories have antioxidants, therefore wood pulp suppositories are good for you - that's pure junk science. It's really heartbreaking and at the same time really pisses me off when someone with a cancer diagnosis (often early stage and very treatable) decides to go the alternate route - only to show up on the doorstep a year or two later with stage IV disease hoping we can magically fix them.
A quick search on the national institutes of health database (pubmed) will not bring up a single study of coconut oil and alzheimers. There is a study done in Korea that a coconut oil-derived compound might have an effect on glucose level - that would be one of those tangential stretches I call bull E36 M3 on to apply it to alzheimers.
On the positive side, it's considered safe for cosmetics and food use. The people's pharmacy says it might be helpful for Crohn's disease or Irritable Bowel Syndrome in the form of a coconut macaroon a day. Other than spending money on it, there's probably no harm (if you're not allergic to it) in taking amounts you'd find in a serving of food.
Have a cookie, by the time you finish it, you'll feel right as rain...