No. When in GameCube mode, the system cuts off all access to the Wii's hardware that would make this possible, such as the USB ports. There has been some progress on a USB Loader, but last I read the guy behind it has hit a huge snag. The people on these forums see someone asking about a GameCube USB Loader almost every day, so expect some snarky comments if anyone else replies.
Use the search function next time.