Redox Flow Batteries (RFBs) are a promising technology for grid-scale electrochemical energy storage. In this work, we use a recently achieved high-performance flow battery performance curve as a basis to assess the maximum achievable performance of a RFB employing non-aqueous solutions as active materials. First we show high performance in a vanadium redox flow battery (VRFB), specifically a limiting situation in which the cell losses are ohmic in nature and derive from electrolyte conductance. Based on that case, we analyze the analogous limiting behavior of non-aqueous (NA) systems using a series of calculations assuming similar ohmic losses, scaled by the relative electrolyte resistances, with a higher voltage redox couple assumed for the NA battery. The results indicate that the NA battery performance is limited by the low electrolyte conductivity to a fraction of the performance of the VRFB. Given the narrow window in which the NARFB offers advantages, even for the most generous limiting assumptions related to performance while ignoring the numerous other disadvantageous aspects of these systems, we conclude that this technology is unlikely under present circumstances to provide practical large-scale energy storage solutions.