Of the successful founders I know personally, each and every one is incredibly risk averse in anything ancillary to the startup itself.
Under that assumption, trying to think of answers isn't any better than a random guess. And I was asking the question for that specific situation, even if it's unlikely, just to know how things could potential be. Furthermore, in the case the government doesn't know about your staying illegally, you would be the same as any random non-citizen trying to immigrate to the US, and it's fairly safe to say that the task is non-trivial (paperwork-wise). In that case, it would still be helpful to know if a founder-but-can't-tell-government would have any advantage at all.
Not every question can be answered by just thinking hard enough, especially those related to laws - that's why there is a whole profession dedicated to it. And it will serve you well to be more careful before going passive-aggressive.