By "with a kid" do you mean trailer, trail-a-bike, or kid on their own bike?
I think it looks not ideal but do-able, the shoulder seems to run the whole way and you can pull off in the grassy area if necessary. You'd want bright colors, flashy lights, and a flag.
I would not do it in the winter if there is any significant snowbank. But since you live in NC I'm guessing that's probably not an issue.