The way that Wii games like that were able to read GameCube save files was from the physical memory card in the actual GameCube memory card ports on an original Wii. Wii U has no GameCube memory card ports, so Nintendont instead has to emulate a memory card, usually saving it to SD card as a .raw file -- depending on your settings, it will either get its own emulated memory card just for it or reside on a shared memory card with all other games of the same region.
Basically, the answer is no, if you inject a Wii game on the Wii U menu it's not going to be able to read GameCube save data.
It might be possible to somehow patch Radiant Dawn to check the SD card where the GameCube save file is located instead, but that's not something I'd know how to do. I'm also not sure how the Virtual Console IOS works, if that matters, so I also couldn't say whether this patched Radiant Dawn would be able to read the GameCube save if it's injected -- you might have to play this hypothetical patched Radiant Dawn via a loader in vWii mode instead.
Another, easier solution would simply be to take that .raw file from the GameCube save and import it into the Dolphin emulator, then load your Wii game in Dolphin and have it read the data. Assuming the game only needs to check your save data once, rather than repeatedly, then you could transfer that save data to SD card in the appropriate subdirectory and use the vWii menu to move the save data onto your system, and then play your injected Radiant Dawn that way, since injected Wii games still save to the vWii's normal storage the same as any disc-based Wii games you play on Wii U.
