Can a shader extend flat geometry (eg. a plane), giving it depth?

Many impressive shader solutions (eg. Curved World) have made me realise that some geometry warping effects are achievable.

I have hopes to improve my shader knowledge to learn how to extend a plane along it's face's normals. In other words, a 1x1 plane with the shader could extend out along an axis (world or local, either) to appear to be a 1x1x1 cube. My currently design style does not require textures, or even lighting (flat pseudo-lighting is achieved through varying colours), which may add to an easier solution.

If anybody could offer insight into if this is possible, and any tips on what to look into to achieve the effect, it would be much appreciated. Depending on the processing required to achieve a shader-based solution vs. actually building the mesh, I'm interested in knowing my options.