Coincidentally, I just rode this route on Saturday. I didn't get run over, so it is possible to do it safely.
To add to what HandsomeRyan said, part of Campbell Station between I-40/75 and Kingston has a small shoulder/sidewalk alternative, but part of it doesn't. South of Kingston Pike there is a sidewalk if you want to ride it. The road is fairly straight with room for vehicles to pass. If you are comfortable riding with traffic, it's doable.
North of I 40/75, traffic is dramatically lower. But there's no shoulder and there's more curves (worse visibility). Moreover, you have to climb over a ridge. So there's a good chance you'll have a truck or two roar by you as you plod up the hill. Sometimes that kind of riding feels
more dangerous than high-traffic roads.