Not necessarily. There are science fiction stories about extension of youth without extension of lifespan, and ancient myths about people cursed to live a long time without youth.

It's possible to imagine health-extending treaments (artificial joints and organs (heart), lung flushes) that don't extend lifespan). We already have treatments that can extend people's lives without health. (Unsuccessful chemotherapy, for one; insulin for type 2 diabetes mellitus, for another.)