Rick, I mostly walk but occasionaly run during my trips. I've run in golite Jam2, Golite Ion and Granite Gear Virga. I dont think they are packs that are designed for running but all worked well. The main trick is minimizing pack weight. I would think the southern portion of AT in summer would be a great place to try it.
One thing to consider is you should be able to easily cover 100 miles in 5 days by just walking full days during the summer. I'm not in the best shape and have found it fairly easy to walk 10 miles by 11:00 am and be 20 miles by 3:00 pm if I constantly move (just walking) which will leave you 4 to 5 more hours of solid daylight. Granted the terrian can not be too severe for this (for me at least). I have heard that some sections of the southern AT can be tough (Blood Mountain).
The thing is minimize your pack weight and keep everything simple so setting up camp is fast and breaking camp is faster. For example …a tarp (6.5 oz), bivy (6.5 oz), pad (4 oz), quilt/bag (16 oz) + stakes and line (3 oz) should weigh around 2.25 lbs total (in GA mountains summer). Add a simples alcohol stove and mug if you want hot food and you might get away with not even taking an insulating layer. You could easily put together a 5 to 6 lbs gear kit that will take you the entire way. Add 20 oz food/day….=6.25 more pounds plus water. Carry under 1 liter (2 lbs) of water at anytime and the most you have on your back is 15 pounds at the start of the trip.
Bring a watch to wake up before dawn so that at first light you are on the trail and you will be surprised how far you will go by lunch time. Ray Jardines book "Beyond Backpacking" has a chapter that teaches you how to cover 30 miles a day by just walking. It is out of print and impossible to find (try the local library…thats where I got my…its on its 5th renewal).
In the end I've found that my distance covered has increased much more by knowledge then actually physical conditioning or speed on the trail. At the age of 40 using lightweight techniques I easily cover 2x to 3x what I did at the age of 20 using traditional techniques.
Jamie