Can a person who was mentally healthy present with moderate symptoms of alzheimer's following several infections?

Yes: Symptoms yes, Alzheimer's no you are most likely dehydrated may need to rule out a small stroke if the symptoms are severe.

Yes: Often the symptoms of early dementia go unrecognized. After a significant illness or general anesthesia there can be a notable and very obvious change in cognition so that is often when the diagnosis is made. However one needs to be vigilant for delirium which can mimic dementia or be present at the same time. See an experienced geriatric psychiatrist for evaluation if this occurs.

Infection = delirium: If someone was previously without cognitive trouble, they won't suddenly develop alzheimer's or another dementia with an infection. A sudden change in cognition is called delirium and may be directly related to the infection and/or the medications used to treat them. Once the infection and treatment ends, cognition normally returns to prior baseline.