it depends on what kind of emulator it is. in order for other controllers to work besides the wii remote, it is necessary to code the controller driver into the emulator itself, because the wii itself does not support such controllers. I'm not into emulators, so I don't know if there are any other than Nintendont. if it exists, it will probably be written on the homepage of the emulator you are using.
EDIT: found this gbatemp thread about 3rd party classic controller working on FCE Ultra GX so if that controller used xinput you might get 8bitdo working. just try plug it in and see if it works, you have nothing to lose.
thread:
https://gbatemp.net/threads/fce-ultra-gx-nes-classic-controller-support.457917/