Your 200 is plenty to move along fast enough on the parkway. You will want to bring along a gas can or you will certainly run out of gas during those long gaps between stations. It can get boring during the many 35mph sections with little scenery.
It can also get pretty dangerous between the old people going 25mph and the motorcycles cutting corners at 80mph. I lived near Asheville North Carolina and we used to see all the crashes on the news during leaf season.
