Does the Sun have a Shadow?

If he meant, does the sun cast a shadow visible here on earth (or any other planet, for that matter), the answer is no. It is the light from the sun which makes other objects throw shadows. In order for the sun to cast a shadow, it would have to be backlit by a brighter, more powerful object.

Does he?

An equivalent analogy would be the shadow if a lit lightbulb. Inherently, as far as visible light I would say no, but the inner surface of the balb does attenuate the light before it passes through the membrane. Similarly, the inner mass of the sun (or in your son's case--son) does attenuate the inner incandescence before it exits the sun, but this attenuation is not what I would consider a shadow.

Another way to look at this is like hot vs cold thermodynamically. i.e. there is no such thing as cold, there is only less heat, and the surface of the sun if hot, but the interior is really hot.

Rap

I suppose if your son were in college, you might answer that the sun's gravitational pull distorts star-light and so creates a "shadow".

When Venus is on the far side of the Sun, the light from Venus
may pass right by the sun and be blocked by it.

The Venus-light would be bazillions of times fainter than Sun-light,
but it would indeed have a shadow caused by the Sun blocking it's way.