Your employer will not be notified. Don't waste even a moment thinking about it. Even if your employer provides the insurance, there are laws that protect your medical privacy. It absolutely will not happen.
Two things I am tired of typing: 1.) A wrongful termination does not mean that you were fired for something you didn't do; it means that you were fired for a reason prohibited by law. 2.) The above answer, whatever it is, assumes that no legally binding contract or CBA expressly says otherwise. If it does, the terms of the contract apply.