Get visible vertices?

I would like to change the color of mesh vertices that are visible to the camera.

Could this be done with a shader?

That is, could a shader report which vertices are visible to the main camera in such a way (perhaps by returning vertex index number?) that would allow me to then change the color of those vertices permanently using a script?

Or, is this something best done without shaders?

So far, I've only come up with the rather inelegant and inefficient approach of checking whether each vertex in a mesh is within the viewport (but this doesn't take into account whether a vertex is occluded).

Thanks hugely for your thoughts!