Depends how soon the dementia follows. I'm not sure if living is so good with severe dementia. Actually, if it's very severe then you're probably OK - my mother has a complex dementia and her medical team have now found a drug regime that "works", unfortunately that makes her more lucid and aware, enough that she has become severely depressed. Looking in on her condition I think I'd find death a welcome end if it were me; there's a strong sense of being locked in.
Whilst our instinct is to live on I'm not convinced that is always right.