Is the shadow ray in a Whitted ray tracer occluded by transparent objects?
You should first refer to Rendering Equation. It is the general equation to describe the physically transmitting of light in the view of computer science.

Whitted model is just an approximation of the surface integration of the Rendering Equation. It only calculates three light rays(shadow ray, reflected ray, and refracted ray). In a more sophisticated ray tracer, you should use Monte-Carlo ray tracing, where at every intersection point on the object, you will use thousands of rays sampling according to BRDF. Such backward algorithms actually work not good at caustic scene, which is the scene you say. You can use Photon Mapping plus Monte-Carlo Ray Tracing to get a better visualization.

If you just want to use Whitted model, you can multiply the lighting of shadow ray by a factor defined by the occluded transparent object.