If I fed it a signal through the optical input and output to my headphone amp through the RCA output wouldn't I have the option of using either the SS or tube output? Doesn't this unit have two sets of RCA outputs one using the SS circuit and the other using the tube circuitry?
Right. Only the pre-amp outs on the D1 have the tube sound.
Since you already have the Little Dot MKIII, why would you want to do that? Why not just buy a good transparent DAC and trust in your tube headphone amp? Get an ODAC and convert your music to digital files.