It would. Look through the shadow cam of an infinite light, by default you'll see the whole scene, including the skydome.
You can manually reduce the area that the shadow map has to cover using the zoom and pan dials of the shadow cam, or you can switch to raytraced shadows. My personal preference is raytraced shadows. Slower, but more accurate, no matter the size of the scene, and they tend to use less RAM.

The pen is mightier than the sword. But if you literally want to have some impact, use a typewriter

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