It is not really that great of a drive. Lots of turns in a short road. The roads around it and the Blue Ridge Parkway are far better. There are roads in Arkansas that are orders of magnitude better than the dragon tail. There is one road in NE Arkansas that goes into Missouri that is so curvy it made a lot of the drivers car sick, and that road goes for miles and miles. We took one road out of Clarksville north and after an hour we had not seen one other car except the ones in our group. The only bad part was when we finally got to a business with a restroom it was just a single bathroom and we had 18 cars and almost all the cars had a couple.
The Dragon is worth doing if you are going to be in the area or if you are going with a fun group of people. I would not make it a single destination trip.
When I went through I saw the photographers but there was not a good place to turn around. I finished the tail, turned around and stopped for the contact info to buy the photo. Finished that direction and then I went back the other direction to get to my destination. I am glad I went but it was only because it was right on the way.