No. The second law of thermodynamics states that high-entropy states are more likely than low-entropy states. Quantum immortality means that you can only observe a state where you're alive. In combination, you're more likely to observe a high-entropy state where you're alive than a low-entropy state where you're alive.
That is, under quantum immortality, your body will keep accumulating non-lethal damage and your suffering will never end. It's quantum immortality, not quantum eternal youth.
But the thing I don't understand about all this is that if the many-worlds interpretation accepts quantum immortality then wouldn't that collide with the second law of thermodynamics?