Not that I know of. Nintendont (for Gamecube games) is the only Wii software that supports that adapter AFAIK.
Nintendo's Virtual Console software only works with the built-in/proprietary controllers: Gamecube or Wiimote(-attached). One of the homebrew N64 emulators might support some USB controllers, but I doubt they support those 4 port gamecube adapters (which were designed and released for WiiU and on).