USBLoaderGX will not detect or use it as a Gamecube controller when inside the loader. (real controller can be used in the loader's interface, but not USB controllers).
Like greywolf said, USBLoaderGX is not related with the controller compatibility when playing a gamecube game.
what you need to verify, is if the Gamecube loader is compatible : Nintendont. (the homebrew responsible for interfacing the console hardware with the gamecube ISO in real time)
Nintendont is compatible with "HID-USB" compliant USB controllers. What you need to know is if your controller is "HID" (Human Interface Device) or not.
There's a homebrew you can launch to see if your controller is HID.
you can find the link and help in Nintendont thread, first post.
If it works, then you either are lucky and all the buttons are "the most commonly used" and it just work, or unlucky and you will have to create a button mapping file, to link each controller buttons to the gamecube button.