We have extended an effective medium approximation theory [Fishchuk, Kadashchuk, Genoe, Ullah, Sitter, Singh, Sariciftci, and Bässler, Phys. Rev. B 81, 045202 (2010)] to investigate how polaron formation affects the Meyer-Neldel (MN) compensation behavior observed for temperature-dependent charge-carrier transport in disordered organic semiconductors at large carrier concentrations, as realized in organic field-effect transistors (OFETs). We show that the compensation behavior in organic semiconductor thin films can be consistently described for both nonpolaronic and polaronic hopping transport in the framework of the disorder formalism using either Miller-Abrahams or polaron Marcus rates, respectively, provided that the polaron binding energy is small compared to the width of the density of states (DOS) distribution in the system. We argue that alternative models based on thermodynamic reasoning, like the multiexcitation entropy (MEE) model, which assumes charge transport dominated by polarons with multiphonon processes and ignores the energy disorder, are inherently not applicable to describe adequately the charge-carrier transport in disordered organic semiconductors. We have suggested and realized a test experiment based on measurements of the compensation behavior for the temperature-dependent conductivity and mobility in OFET devices to check the applicability of these models. We point out that the MN behavior observed in thin-film OFETs has nothing to do with the genuine MN rule predicted by the MEE approach, but rather it is an apparent effect arising as a consequence of the functional dependence of the partial filling of the DOS in a disordered system with hopping transport. This fact is fully supported by experimental results. The apparent MN energy was found to depend also on the shape of the DOS distribution and polaron binding energy.