I can think of at least one highly successful person (Creator of several household name open source projects), who has dealt with rather serious chronic health conditions throughout their life. Won't name names since it's a somewhat sensitive subject.

For an example from the business world that is a matter of public record, Steve Jobs was diagnosed with Pancreatic Cancer in 2003 and he still had an active role in the development of the iPhone and iPad before eventually dying in 2011.