Yes.  Look up the old literature on different methods of measuring diffusion and centrifugation, the 1950s optical methods,.  There are at least iirc three of them. See Schlieren optics and Guoy optics for two.  There was also a 1950s gadget, the Beckman diffusion-electrophoresis apparatus, that was commercial, though no longer made when I gained one in 1978, that did what you ask.

Basically the interferometer is going to measure any change in the index of refraction of your sample, so anything that changes this can , phenomenolgically speaking, be measured.  As the index of refraction is material dependent, changes in concentrations in complex liquids lead to changes in density, lead to changes in the index.  So the simple answer to your question is yes.  I heartily agree with George Phillies's answer above and would also add that you look at mixture formulas for the interpretation.  I would recommend the following article for a short introduction to mixture formulas ', Stoneman M. et al. Bioelectrochemistry, 2007. 70: p. 542-550.  The mixture formula will allow you to prize out the contribution to n involving one of your components when the index behavior of the solvent is known.