NMR spectroscopy studies using parahydrogen-induced polarization have previously established the existence of the pairwise hydrogen addition route in the hydrogenation of unsaturated hydrocarbons over heterogeneous catalysts, including those based on rhodium (Rh0). This pathway requires the incorporation of both hydrogen atoms from one hydrogen molecule to the same product molecule. However, the underlying mechanism for such pairwise hydrogen addition must be better understood. The involvement of carbon, either in the form of carbonaceous deposits on the surface of a catalyst or as a metal carbide phase, is known to modify catalytic properties significantly and thus could also affect the pairwise hydrogen addition route. Here, we explored carbon's role by studying the hydrogenation of propene and propyne with parahydrogen on a Rh2C catalyst and comparing the results with those for a Rh0/C catalyst obtained from Rh2C via H2 pretreatment. While the catalysts Rh2C and Rh0/C differ notably in the rate of conversion of parahydrogen to normal hydrogen as well as in terms of hydrogenation activity, our findings suggest that the carbide phase does not play a significant role in the pairwise H2 addition route on rhodium catalysts.