Dr Yong in the paper titled Prion, The unconventional slow Infectious agent states that the formation of amyloid plaque which is a major contributor to Alzheimer's disease is a unconventionally slow infectious disease (Prion). Some papers have also pointed out the similarities between Alzheimers and prion disorders (reference) Cerebral amyloid plaques have also been identified in scrapie which is caused by a Prion. Discovery of a novel prion disorder (reference) with peripheral symptoms have led researchers to believe that protein misfolding, is the basis for most neuro-degenerative diseases, including Alzheimer's disease and Parkinson's disease.
With regard to your question, Alzheimer's has not been completely classified as a prion disorder as of now, but seeing that amyloid plaque formation (reference) and Creutzfeldt-Jakob disease (CJD) (a form of dementia) (reference) have been identified as being part of Prion disorders, it is highly likely that Alzheimer's is too.