We illustrate the effects of chain connectivity on the solvation energy of ions immersed in polymer liquids by developing a new coarse-grained molecular dynamics simulation. Our theory accounts for the dielectric response of the polymers through the connection of dipolar, monomeric units with nonlinear springs. In stark contrast to the standard Born solvation energy of ions, our results depend substantially on the chain length of the polymers. We also demonstrate the marked difference in the solvation energies of the ions immersed in non-polymeric particle mixtures, single-component polymers, polymer blends, and block copolymers. Thus, we suggest that the chain architecture of polymers is a key factor in ion solvation, whereas this feature is often inadequately considered in main theory and simulation literature. Our results are consistent with those predicted by previous coarse-grained mean-field theories when the dipole moment of the polymer compositions is relatively small. However, we also demonstrate that the strong ion-dipole and dipole-dipole interactions cause the chain-like association of the monomeric units, resulting in a qualitative discrepancy between the mean-field theory and simulation. Such a strong electrostatic correlation may reverse the dependence of the chain length on the solvation energy of the ions in the polymers.