You question is missing a very important piece of information: What makes you think that past illness is something that'll scare off employers? In other words, what happened, and how did that affect you?
Why do you seems to think that makes your past murky? I mean, I don't envy you, it's a horrible disease, but it doesn't make your past murky.
I don't think anyone will consider me unreliable, but for someone going through a stack of applications it's something that sticks out for the wrong reasons.
Plus, an application can be seen by a lot of people and you don't want to start a new job being THAT guy. I don't mind people knowing, but I like to have it on my terms if possible.