Does the upper subconscious mind dream during the sleep interval?

This is, indeed, the case. The differentiation and compartmentalization occurs because of the conscious mind being switched off, so it will not witness what the subconscious is thinking about. Dreams are more a free-form thought stream, unencumbered by a conscious oversight and control to set an agenda and change focus as it does, being ever restless. As soon as the conscious mind quiets during the onset of the sleep interval, the upper subconscious is freed up to ruminate on what it chooses and, in fact, never rests.