Obviously in general you can say that Bashir was hiding some of his more advanced abilities (like racketball, tennis, dart throwing, rapid mental calculations) all of his life. But I think that he probably never really held back when working on medical problems. He would never have been OK with people dieing just so that he could keep his genetic enhancements secret. I think that his memory skills and hand-eye-coordination, etc, all those skills that made him a great doctor, had been enhanced to a great level certainly, but not to a level beyond possibility for a non-enhanced person.
Laypeople understand so little about medicine anyway. Most laypeople see doctors as already amazing and magical. No matter what outrageous things he does (like bringing people back from the dead; mentioned early on in "The Passenger") most people will just think he's just like all other doctors. It's only when he does things to get the attention of other doctors (like graduating at the top of his class would have; or like being the youngest person to be nominated for the Carrington Award in "Prophet Motive") that he needs to worry too much about what he does in medicine.
It's the enhanced non-medicine things that he does that cause him more problems.