This is a very difficult question to answer. The time of year, weather, your physical fitness, and backpacking experience would determine this. As a general rule 3 miles per hour plus an additional 1 hour for every 1000ft of elevation gain is a good estimate. If you have some experience you should be able to estimate as to what rate you beat (or exceed) this "book time". Plan you route and see if the amount of time necessary moving each day fits your comfort level. The AT in the Smokeys is rugged and wet. I would recommend just doing a few different overnights on the AT to the Huts and throughout the park such as up to LeConte and day hike Chimney Tops (i think thats whats it called). There is much to do without the commitment of section hiking.