They do and they don't.
My initial plan was to create a rendering as seen from right at the surface, only tens of meters from the ring floor, looking up toward the horizon at the ring, as it swooped out of the atmospheric haze skyward towards the Sun. This would let me experiment with some cool atmospheric shaders and make a cool terrain shader for the ring surface.
The stumbling block I came up against was one of numerical precision: the Ringworld is just too big! The software I'm using is based on the Renderman interface. Renderman likes to traffic in single precision floating point numbers, giving about six digits of accuracy. To get really interesting atmospheric effects, I'd need to be able to work with spaces on the order of, say, 1 kilometer or less. But the Ringworld is 1.53e8 km in radius, eight orders of magnitude bigger! Clearly, six digits of accuracy wasn't going to cut it. So in the end I had to settle for rendering images of the Ringworld as seen from space.