We investigate whether the electric field gradient (EFG) at an atomic site in the unit cell of a periodic solid can be modeled via the electrostatic field gradient set up by atomic point charges outside that site. To test this approach we contrast the EFG predicted by such point-ion models for long-range ordered GaInP2 alloys with the results obtained from self-consistent all-electron calculations in the local density approximation (LDA). We first tested our LDA approach for ZnAl2O4, for which experimental data exist, finding the quadrupole coupling constant Q(cc)(Al-27)=3.94 MHz, compared with the measured value of Q = 3.68 MHz. Applying next the LDA approach to perfectly ordered GaInP2 (for which experimental data do not exist), we find the LDA quadrupole coupling constant Q(cc) = -4.83, -2.84, and 13.08 MHz for Ga-69, Ga-71, and In-115, respectively. We further find that more than 95% of these EFGs originate from the anisotropic electron charge distribution within a small sphere of radius similar to 0.2 Angstrom about the respective atomic site. Hence, the point-ion model significantly underestimates the magnitude of the EFG (and in some cases also gives an incorrect sign). The point-ion model also fails in reproducing the relative trends in the EFG as the crystal structure changes. We conclude that the point-ion model is not a viable alternative to calculate EFG in periodic covalent solids.