Ahhh great question. First, the second question. The Doctor simply sends you to a regular lab with a requisition where you smile and wave at the lady attendant.
I've never been to the clinic, but my understanding is you skip the lab process so save the extra pair o judging eyes.
Now on to the first question, What the clinic's don't readily publish is all
testing information goes into your medical record which your Doctor, or any Doctor (including your Optometrist even - trust me I know 100% fact) has full access to.
The Doctors must have access to your medical history in order to properly diagnose conditions and select treatment suited.
The Doctors may ask you about history however they do not rely on just that info because the patients cannot be expected to know or always remember what is important to communicate.
And so, the Doctors would review your history as part of normal procedure, and not while their with you necessarily, typically it can be before and or after your visit with them.
So if you go to most any clinic there's a high probability your Doctor will learn about that, highly unlikely they would not unless you never see your Doctor for anything else,
and what do you think their conclusions will be then?