When I was first diagnosed with kidney problems it took a couple of months to get the full diagnosis, and I did not tell my immediate family until I knew the full SP. Friends and non-immediate family had to wait about another six weeks as I announced it at my 50th Birthday party, which kind of put a dampener on the festivities. However my boss I told the day after I knew. This was because I was going to need to take lots of days off for tests. It only seemed fair that he knew why. (His reaction was "Well that should not be a problem, just save up the money I pay you, then go to Turkey and buy a new one.")
There have been a few times where I have had my own company (yes, I have several failed businesses behind me, I believe that qualifies me to be president of the USA). I never had any sick staff, and I never thought to come up with a policy in case I did. But if I had (and this is what I think I would have done back then, without the experience of being in that position) the policy would be: If they came to me and explained, and they wanted to continue to work for me, I would have moved heaven and earth to sort out a work schedule to fit in with their medical needs. But if they did not tell me, just kept taking time off without explanation, I'd fire them. And if they later came back to me and said "Sorry I was ill" I would have replied "You should have told me and we could have worked something out. But you didn't. So - that square thing in the corner is the door, don't let it hit you in the ass on the way out."
Having been sick myself for some time, if I opened a new business now, that would still be my policy. If someone is paying you a salary, and it effects their business, you owe them the truth.