Enhanced whistler mode waves produced by anisotropic hot plasma-sheet electrons outside the storm-time plasmapause have been suggested as one mechanism for accelerating relativistic outer-belt electrons in the aftermath of geomagnetic storms. Using measurements from the Los Alamos Magnetospheric Plasma Analyzers in geosynchronous orbit, we perform a superposed-epoch study of the storm-time behavior of the inferred plasma-sheet whistler growth parameter. Separate analyses are done for storms that result in strong relativistic electron enhancements and those that do not. The inferred whistler instability is strongest in the midnight-to-dawn sector, where freshly injected plasma-sheet electrons drift into and through the inner magnetosphere. During the main phase of both sets of storms, there is a marked drop in the whistler growth parameter, especially in the prime midnight-to-dawn sector. In the early recovery phase, this parameter is elevated and then returns to more typical values over the next few days. The elevation of the whistler growth parameter persists longer for the electron-enhanced storms than for those that do not produce such enhancements. These results suggest that whistler wave generation is greater during storms yielding enhanced levels of relativistic electrons.