No. You can begin dual flight instruction BEFORE you take the FAA Medical.  You must take and pass the medical before you are trained and authorized by your flight instructor to fly the helicopter solo (that is, by yourself).  The physical is very quick and easy.  It consists of a eye test (like the driver's license test) and a very simple physical exam from an FAA-trained doctor, called an Aviation Medical Examiner (AME).  Unlike in the military, there are VERY FEW medical (or eyesight) conditions that will prevent you from getting a civilian pilot's license.  If you have a serious medical condition that you believe MIGHT prevent you from obtaining an FAA Medical, you should consult with an a FAA-approved doctor (called an AME, or Aviation Medical Examiner) BEFORE you begin Flight Training.  The Private Pilot Physical is good for two or five years, depending on your age.  You can find the names of local AMEs on the FAA's website.