There may be benefits of being bilingual. Several studies have shown that if you know two or more languages — and you've been diagnosed as likely to develop Alzheimer's — you may experience a delay in the onset of Alzheimer's symptoms. Researchers believe being bilingual or multilingual helps develop your brain's "cognitive reserve" in the same way that engaging in other mentally and socially stimulating activities does.
More research is needed before it's completely understood how cognitive reserve works to delay the onset of Alzheimer's disease and other dementias. It's thought that activities that develop cognitive reserve work because they increase the robustness of your brain's architecture — enriching blood flow, enhancing neuronal activity and putting more of your brain to use. This may compensate for the loss of diseased parts of the brain.
Engaging in a variety of activities, especially those promoting mental and social stimulation, may help people at risk of developing Alzheimer's disease or dementia slow or delay its onset. And if you're interested in learning another language, go for it. However, more research is needed before it's known whether learning a second language later in life has the same protective effect as might a lifetime of speaking a second language.