There are two potential ways that Rapamycin could affect the onset or progression of Alzheimer's. The first is through induction of a cellular process called autophagy. Autophagy is the process through which intracellular material is broken down and recycled. In some settings, Rapamycin is a potent inducer of autophagy. Rapamycin induces autophagy by inhibiting a signaling complex called TOR; active TOR signaling inhibits autophagy, so inhibition of TOR affectively induces autophagy. Increases in autophagy could lead to an increased clearance of amyloid beta and tau, slowing the formation of plaques. There is a significant amount of literature supporting this thought. Many labs using a variety of models have shown that increasing autophagy is beneficial to a number of models of proteotoxic stress. Given that symptoms do not appear in Alzheimer's patients until significant cell death has already occurred a lot of work needs to be done in the field of biomarkers of Alzheimer's before the affectiveness of Rapamycin in human patients can even be tested.
The second way that Rapamycin could help slow the progression of Alzheimer's is through it's immune modulating affects. The question of whether amyloid plaques in Alzheimer's actually cause cell death is still unanswered. Some research indicates that cell death may be occurring through an immunological pathway (specifically through activated compliment mediated neuronal cell death). If Rapamycin were to modulate this mechanism of cell death it may also alter the progression of Alzheimer's disease.
TOR signaling and Rapamycin are a major focus of study among biogerontologists, and are being actively researched as targets for the treatment of a variety of diseases.