We present a comprehensive study investigating the potential gain in accuracy for calculating absolute solvation free energies (ASFE) using a neural network potential to describe the intramolecular energy of the solute. We calculated the ASFE for most compounds from the FreeSolv database using the Open Force Field (OpenFF) and compared them to earlier results obtained with the CHARMM General Force Field (CGenFF). By applying a nonequilibrium (NEQ) switching approach between the molecular mechanics (MM) description (either OpenFF or CGenFF) and the neural net potential (NNP)/MM level of theory (using ANI-2x as the NNP potential), we attempted to improve the accuracy of the calculated ASFEs. The predictive performance of the results did not change when this approach was applied to all 589 small molecules in the FreeSolv database that ANI-2x can describe. When selecting a subset of 156 molecules, focusing on compounds where the force fields performed poorly, we saw a slight improvement in the root-mean-square error (RMSE) and mean absolute error (MAE). The majority of our calculations utilized unidirectional NEQ protocols based on Jarzynski's equation. Additionally, we conducted bidirectional NEQ switching for a subset of 156 solutes. Notably, only a small fraction (10 out of 156) exhibited statistically significant discrepancies between unidirectional and bidirectional NEQ switching free energy estimates.