This depends on the stage. If someone is newly diagnosed, I would think they could, but it's possible the attorney would want a doctor's opinion before allowing it. If someone is several stages in, it may not hold up in court. I'd enlist the doctor and an estate attorney for this work.
This is an interesting and very complex area-assessing the competence of someone with Alzheimer's disease. There has been quite a bit of research because people with Alzheimer's disease who take part in research studies, have to consent to treatments.
Even people with relatively mild Alzheimer's disease can be significantly impaired to give consent. Many people with mild to moderate Alzheimer's are unable to give informed consent according to the legal criteria. Researchers have found differentiating capable from incapable subjects remains an big issue.
If you are worried that any legal documents that you sign may be challenged since your diagnosis then you need to seek advise from a lawyer.
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