It cannot.

The Monk and the insides of the box are still in the dark. The Monk just perceives them differently.

It is the same as if an illusion made the Monk see light or fire near him. He would still be in the darkness, and would be able to use his Shadow Step.

It cannot.

The Monk and the insides of the box are still in the dark. The Monk just perceives them differently.

To you, solid objects within that radius [...] don't prevent light from passing through them.

It is the same as if an illusion made the Monk imagine he could see light or fire near him. He would still be in the darkness (even if he believed to be in light or something), and would be able to use his Shadow Step.