No. Unfortunately, I am not aware of any direct communication being established with the non-dominant hemisphere. I'm not sure if any such communication would even be possible given the diminished faculties available to it - speech in particular is usually processed in the left hemisphere.
However, the two halves of the brain are both demonstrably conscious. There is brain activity in both hemispheres, and both respond to stimuli in a manner consistent with the faculties they possess. Facial recognition and mathematical capabilities differ between the two of them, for example.
Both sides are conscious, and both sides are independent of one another. The only question is to what extent the non-dominant side retains lucidity given their differing roles.