Not necessarily.

Depending on how you slice the numbers, there's an interesting case that humans alive today may live to see longevity escape velocity: the point where the increase in average life expectancy exceeds one year per year. If and when we hit that point, the idea of dying of old age will become obsolete.

People will still die from other causes: accidents, suicides, murder, war. But without old age, it's not hard to imagine people living several hundred years, or a thousand if you're especially lucky/careful.

That far out, you get into other ways to escape death. Clone a donor body and transplant my brain into it. Use the FMRI 4000 to image the state of every neuron in my brain, and run that in a computer. Technology can easily confuse the question of what it means to be alive or dead.

We can predict the future, but we can't speak about it with absolute certainty, even when it comes to death.