Relativistic Radial Velocities to determine inclination?

I was going back through some older postings on arXiv and noticed this paper, which proposes measuring the relativistic radial velocity of a star to determine the total velocity of the star, which of course can be compared to the radial velocity of the star to determine the inclination of the orbit of a companion.

I don't really understand it myself, but whatever happened to this idea? Does it not work?