I think we all heard negative stories around health issues. Reality is, that the companies I worked with in the past 18 years were positive, understanding an supportive.
Healthy companies hire people for the long term. They are looking for young talent who will go and grow with them. Health issues are hopefully temporary and will go away.
I agree with you that this may be a disadvantage in the first period, because it'll be hard to compare your performance to your peer group. You'll be somehow an exception. It does not sound fair, and I'm not saying it's right. My experience tells me that chances are high that someone else gets the first promotion.
The most important thing for you right now is to communicate openly. Tell your boss on your first working day that some health issues have come up and you are working with your doctor to understand what treatment is needed.
Don't tell her/him anything that has not been decided yet by your doctor. Tell your boss when you expect to know more.
I think your progress at work is not a profitability question. It's not newbies who create or destroy corporate profits (usually). Your cultural fit, attitude and added value will be checked in the first period.
Added value is not necessarily related to the amount of time you spend at work. Good ideas that improve service, products and the way you work are equally important.
Hope your boss will be nice enough to keep you relaxed, it will help you to recover quickly.
If your boss tells you that you are not profitable enough or your health issues are not accepted would be an alarming red light. Keep in mind that you are also assessing cultural fit and attitude in the first period. You cannot control the attitude of your employer, you have to choose wisely.
If they have the wrong attitude it's better to move on.