This is a very interesting question.
The simple answer is if you used an insurance plan to pay for you illness then they know about it.
Lets say you paid cash:
most insurance companies generally let you in with minimal underwriting, once you file a serious/expensive claim then the true underwriting begin. Now they will generally have access to all your files since you want them to pay up. They will go over everything with a fine tooth comb. If they find anything that was not on the application/omitted they have a legal right to cancel your coverage to day one- as of your policy never excited or just not pay.
The kicker is that most insurance companies will generally take some conditions if they are disclosed on the application. A good broker should be able to look at your issues and guide you to the right carrier.
to recap disclose disclose disclose
and is you have any questions disclose once more.