In this work, we demonstrated that the electronic polarizability in full-frequency GW calculations can be augmented by the frequency-dependent fluid polarizability from the SaLSA implicit solvation model to capture the effects of solvent screening in beyond-DFT electronic structure calculations without the need for sampling of explicit water structures. This approach is generalizable to any solvation model and dimensionality of chemical system, and has been tested extensively here for molecular systems that are expected to be most susceptible to the liquid screening effects. The solvent polarizability significantly alters the frontier orbital positions and in particular lowers the energy of all LUMO energies.The change in frontier orbital energies leads to a net decrease in the molecular HOMO-LUMO gaps by 3 -5 eV on average. We showed that solvent screening is central to these electronic structure changes, and that wavefunctions generated from solvated DFT calculations alone do not result in GW frontier orbital energies much different than DFT wavefunctions generated in vacuum. The technique demonstrated here can be applied to quasiparticle energies of electrochemical interfaces in future work, laying the groundwork for beyond-DFT first-principles electrochemistry.