Actually, there's a disturbing side to it as well, beyond just ending up in a disturbing timeline, if you make two particular suppositions. First, let's presuppose that a particular branch under the Copenhagen interpretation exists for every possibility, regardless of probability. Next, let's presuppose that death is a probabilistic distribution; it's not really a guarantee that you'll die at a particular point, but rather that it's simply close enough to certain that it's effectively impossible to avoid it forever under ordinary circumstances. As such, if you maintain continuity of consciousness through any number of quantum branches (for lack of a better term), you will continue to skate past death in more and more improbable ways, because *some* branch somewhere will have such a possibility of survival. Your heart or liver might not fail, your cancer might be treated or go into indefinite remission, your stroke might be debilitating but not lethal. Senescence does not lead into absolute death, as cells spontaneously mutate in a vanishingly improbable circumstance to continue to divide even after their telomeres are trimmed to naught. Even if you attempt to commit suicide, your gun might misfire, or the noose might break, or your cyanide may prove to be denatured. You end up trapped in an eternally ageing, eternally dying body, without even the promise of an actual death to give you release.
Quantum immortality is a fiend.