Alzheimer's disease affects everyone associated with the individual fighting the disease. As the Alzheimer's patient's mind deteriorates, it falls to the people closest to the patient to take care of the patient's needs and safety. Alzheimer's patients have been known to "wander off", or totally lose the ability to recite their name or address. These types of incidents can happen suddenly, without warning, and can cause great harm to the patient. Screening Alheimer's patients frequently for signs of memory loss, or increased disorientation, could possibly avoid future harm to the patient and increase the caregiver's ability to manage the disease.
I don't believe that anyone should be forced to undergo anything, but I believe that it should be strongly advised, at first. If it becomes undeniable that they have Alzheimer's then they should perhaps be forced to undergo a screening. If they have Alzheimer's they might not have the capacity to say yes for themselves.
It should not be required that they undergo medical screening for Alzheimer's, but it would be smart to do so. Alzheimer's can't be cured, and there isn't really treatment for it, so the screening won't prevent it from developing more. It will only let them know if they have it or run a risk of developing it.
While letting people know that they are showing signs of Alzheimer's disease is incredibly important, no one should be forced to be screened. Medicine and treatment for diseases is an option and should always stay an option. Some people prefer the help but that does not mean that everyone is looking to be cured. People should be aware that they have the symptoms but no one should be forced to take action.
While it's good for the sake of their own health to get screened, I think making it mandatory will allow insurance companies to deny people coverage. We've already got problems with insurance companies declining coverage due to pre-existing conditions, and this will only add yet another condition for them to use against people.