Operators are required to have a copy of the pilot's current medical certificate on file. Therefore, only the conditions printed on the medical certificate itself would be visible to them.
Any other correspondence between the pilot and the authority would not normally be any of their business, unless it impacted on the pilot's ability to do the job. But you would not hold a Class One medical if that was likely.
There is a whole range of stuff that an employer is no longer entitled to know - marital status, sexual orientation, religious beliefs etc. The only probe an employer could make would be the usual "is there any reason why you would not be able to perform your duties?" That one has been known to exclude pilots whose religious beliefs prevent them working on a certain day each week.