There isn't much that can be done to prevent the disease, especially if one is already suffering the initial symptoms. Part of our problem with AD and similar degenerative disease is that we don't have a full understanding of what causes the condition therefore it's difficult to say what one can do to prevent it.
As you mention, it has been inferred that an active mind may hold off the appearance of symptoms. This paradigm in laboratory animal studies is called environmental enrichment and has been shown to positively affect many of the negative aspects of aging, disease or toxicity. Some of the theories behind why this is observed speak to increased sprouting of neuronal connections and strengthening of established connections, thus the system is stronger and can take more hits than a weaker, under-used system.
However, while this may possibly gain you a few years, you can't fight the disease this way forever and eventually the degeneration will be too extensive and symptoms will appear. This is not to say that everyone will get AD, or that those who don't use their brain as much as others are more likely to fall victim. If you are somehow predisposed to develop AD or Parkinson's or any other such disease whether by genetics, environment or a combination of both, we currently have little way to identify this predisposition and, as mentioned, little understanding in how to prevent the progression once it is diagnosed. We are typically able to treat the symptoms, but the underlying disease process still continues.
In my mind this is no reason to suspect or live in fear of these conditions, new advances are made all the time and perhaps we will someday understand and hopefully control these conditions. I am all for exercising the mind to improve one's abilities but for now it serves no purpose to focus on the off chance that one might someday be diagnosed with some form of degenerative disease.