What you’re describing is called reflective caustics in 3D parlance. I don’t see a way to enable it for the Sky Object’s sun light, but I suppose you could disable the sky’s sun and use a separate sun light. You would then need to go the light’s Caustics tab and enable reflective caustics. In addition, you would have to add the Caustics effect in render settings.
At the end of the day it may be easier just to fake it. 😉