Learned helplessness can be a part of mental illness and/or result of it...its certainly not healthy. And unlearning it, well that is difficult when its how you developed as a child.......so I'd say in that case the illness and learned helplessness could potentially kill as both probably contribute to things like suicidal feelings and/or self destructive behavior and mental illness can also make people more vulnerable to some health problems.

Not sure how it wouldn't at all be the illness and just learned helplessness alone as I cannot really imagine an instance where one would have learned helplessness without a mental illness since someone with a healthy mental state wouldn't have that issue.