Modeling thermodynamic properties of electrolyte solutions is challenging but needed in various applications. In this work, we probe a recent electrolyte theory that describes details of the charge distribution inside ions. We explore the parameter space of this theory to assess whether it is helpful in engineering calculations. To test the theory, we describe the osmotic coefficients in aqueous solutions of 1-alkyl-3-methylimidazolium halides, ionic liquids that have asymmetric organic cations. These systems have also been described with the aid of two versions of the ePC-SAFT EOS: "ePC-SAFT Revised" and "ePC-SAFT Advanced". Parameters for both versions have been estimated. The densities of aqueous solutions of the studied ionic liquids were measured at 298.15 K and 101 kPa. We show that the "ePC-SAFT Advanced" version works much better than the "ePC-SAFT Revised" version. The new theory appears to be quite flexible: the description of the osmotic coefficients is not inferior to that from "ePC-SAFT Advanced". We also test predictions from theory versus computer simulation for a system of charged hard spheres in a dielectric continuum. Our results motivate further development and broader applications of the models based on the theoretical approach employed in this work.