I'd say it pretty clearly does. If it were a rational decision with no mental illness involved, the person could realize they can just pull a real world "why_". Just disappear, go somewhere else, be someone else and start over where no one knows you. You're going to lose everyone and everything you know anyway, why do you need to actually kill yourself as well (and doing so isn't risk free)?
If the person is rational then problems can only be one of two kinds: situational (e.g. my life sucks because I owe more money than I stand to earn in 3 lifetimes) and health-related. The rational stance to the first kind would be to do as I suggest above. Obviously, in the second case escaping won't change anything so suicide could be a rational choice.
no, i'm dismissing the idea that suicide necessarily means a mental illness.