I believe that once the determination has been made that you have complied with the provisions of your SI, your medical is issued without further notation. It won't say, "Hey, this guy was an alky!" or "Watch out for this one, his last EKG was a little shaky" The SI stuff is all between your AME and the FAA flight surgeon, and any other medical professionals the FAA chooses to employ.

I'm not certain employers are allowed to question prospective employees about their medical history beyond that which is necessary for them to perform their jobs. If the job requires a Class II medical and you have one in your possession, that's all you need. If the job requires a Class II medical, and that you load heavy items into the plane, they can ask you if you are capable of lifting such items. They can't ask you "what you did to get so strong?"