Only death stops stagnation in the end. Without death, especially if death can be avoided by the rich and powerful but not the poor, life will get much, much worse for the average person (until only the rich and their automated capital remain I suppose, in which scenario they will simply turn on each other).
But it's actually the wrong way around. Hope that the despot will soon die saps peoples' will to do the difficult and dangerous job of removing them. Take away that hope and they are forced to find the courage.
Especially true if it is the AIs that get us the immortality- it definitely won't be equally spread, and any incumbents have a massive advantage.
I think more people would settle for worse conditions to stay alive. Do you think you'd be more likely to revolt at 150yrs old when all your family and yourself can live extremely long to forever? Or do you think the threat of death by killing wouldn't be an issue?
Also, if you eliminate all the aging-related causes of death the average lifespan is still only like 1000 years or something. Nobody's getting eternity. And yeah, for the chance to make a big enough change of the right kind to society I would indeed give up a 1000-year lifespan. My memes have fully subjugated my genes, and I'm at peace with that.