Quantum immortality doesn't promise health. It promises consciousness.
It is in fact a horrible idea and you better damned well hope it is false, because it looks a lot less like "I'm going to live forever in at least some fraction of the multiverse and be healthy and happy!" and rather a lot more like SCP-2718 [1]. Probably without the pain in question, but certainly with your consciousness stuck in a body that is literally minimally capable of being conscious and nothing else, past the heat-death of the universe, until the point where even quantum randomness isn't enough to keep you conscious, assuming that such a point can even arrive. QI doesn't protect your mobility, your senses, your health or happiness... just your consciousness. On the plus side, "minimal consciousness" doesn't necessarily entail a great deal of awareness of time passing.
[1]: http://www.scp-wiki.net/scp-2718 , for those not familiar with the format of the site, be sure to click the "► Play" on the bottom for the text I'm referring to. On the topic of SCP, the "End of Death" canon rather resembles your story, albeit moreso: http://www.scp-wiki.net/end-of-death-hub