The health of the CEO definitely has impacts on the company, especially so in Apple's case. The health of Apple is directly related to Jobs, much more so than any other large company I can think of. There was an article (can't remember where) about his first bout with cancer and the struggle he had to stay on the up and up with the SEC. Basically it's his private matter up until it would be likely to affect his performance. It's kind of a grey area, but keeping things disclosed is much better for the company.

It's pretty depressing, but you'd have all sorts of insider trading problems with only a few people knowing you're sick. The people who would know (nurses, doctors, etc) would probably be fairly under the radar as far as that's concerned too.