I filed with the local office in NJ and I did not send in my medical when I sent in my application.
My EAD interview is next month, INS did not mention the medical yet, but I am planning to get it over with, now itself.
Go to the doc if he is going to take a week or two to do your medical you could go ahead and send in your app. If the doc can wrap it up fast, then might as well send in everything.