USB Loader GX (and other loaders) have options to install Wii and GameCube discs directly to an HDD.
Is that what you're looking for, or something else?
EDIT: Just checked WUP Installer, and it has title downloading. AFAIK there aren't any on-system title downloaders for WiiWare and Virtual Console, though that doesn't mean it's impossible. NUS servers don't have GameCube titles, but they do have Wii titles for the Wii U eShop, so it *might* be possible to download Wii games directly in a loader, but the format is slightly different than original Wii discs, so it would need some adjustment.