No. In the English speaking world, "I" refers to the tonic tonality. You cannot have a progression without a tonic, since the tonic is defined as the resolution chord of the progression. "I", in the English speaking world, does not refer the root note of the relative major scale of the key of the piece. For example, in D dorian, the progression Dm - Am - B° - Dm is notated by English speaking musicians as i - iv - v - i, not as II - VI - III - VII - II. I don't disagree with your approach, but what you call things does not jive with traditional nomenclature.