Mark, people do ride that road, early in the morning is the key. The speed limit is low but the road is narrow. After a while, the volume of traffic increases to a constant flow. I choose to avoid it. However, as I said others ride it. I think an early as possible start with a flashing taillight is best. There is road repaving on the NC side. Work is only done at night so you should be fine but I would expect a rough road.
There is water in the bathrooms at Clingman's Dome. It is just up the paved trail at the end of the parking lot a few yards. There is water at the Occonluftee Visitor's Center in the restrooms also. Same for Sugarlands on the Tenn. side.
Remember, this weekend starts the July 4th week and the absolute peak of summer visitor traffic in the Park. Be careful.