No, I don't think that this will occur. What is more likely is that several major governments will buy the research instead and simply give away the treatment.
The reason I say this is that a person with Alzheimer's Disease costs money to look after. Even if the state isn't paying, then the person is still going to be a drag on the State since people who are looking after the dementia sufferer are not doing other things which would be producing tax revenue. Whichever way you slice it, demented people are a drain on the resources of a State.
However, if a government subsidises a partial cure or prevention system for Alzheimer's Disease, then several things happen. Firstly, fewer people get dementia before they die of old age, so the costs of caring for the elderly are reduced. Secondly, the government acquires an air of beneficence, which is politically good for them. Thirdly, research like this also ties into other research into other diseases.
By way of illustration of point three, there has over the last fifty years or so been a great reduction in heart and vascular disease. Part of this can be attributed to reduction of smoking (and switching from smoking tobacco to vapes), but by no means all the reduction. Some of the reduction is down to removing various toxins from the environment, such as coal smoke and lead in petrol (gasoline). However, what if living conditions have reduced the incidence of a background infection which was also contributing to the problem? Shouldn't we be on the look-out for things like this?