The major impediment when riding the Parkway in July are the hordes of slow going tourists. I'm talking about motorhomes doing a steady 35mph, Floridians slowing to 30 for each and every curve, and formations of Harleys making much noise but often going even slower than the rest of them (forgive me).
If you drop down to Asheville on I-26 and pick up the BRPW there, you can expect the first 100 miles to be as described - especially on Sunday (Monday is a bit better). Once you are north of Boone, NC it clears out considerably.
The 105 mile long Skyline Drive, which begins in Virginia where the BRPW ends is even slower with a posted speed of 35mph and tourists from the greater metro DC area.
After all that ranting though, I must add that if you or any of your riding buddies have never done the Parkway you should not pass up the opportunity. It is stunning. Just don't expect to be able to maintain 45-50mph.
I have ridden the entire length of the Parkway (Cherokee, NC to Rockfish Gap, VA) in a single 17 hour day, but it sure wasn't in mid-summer.