It does not sound like your question pertains to what the FAA can find out, but rather what an employer can find out. Your personal medical information is protected under
HIPAA (Health Insurance Portability and Accountability Act of 1996), and there are stiff penalties if a medical professional releases your information without your consent. Your personal medical information can probably be obtained through legal means (subpoena) by the government if for example the FAA wanted to pursue a false medical application. Your employer however does not have that kind of legal power.
On the other hand, your application for a medical certificate is not protected by HIPAA. That information is the property of the FAA and they can do with it as they see fit, although it is protected. Again your employer does not have the legal means to access this. If you have real concerns that your medical history contains something that could damage your career in the future it is probably best to get the opinion of a lawyer. Maybe
@MidlifeFlyer in the Aviation Attorney section could shine some light here?
Aaron Florkowski, MD
FAA Designated Aviation Medical Examiner
www.kansascityame.com