You can, and I summed up some of the info in my
blog post about GameCube controllers.
In order to play wirelessly, you need a PC running
Pairing App, running Windows, Linux or even macOS, as well as a Bluetooth receiver capable of handling Bluetooth Low Energy (BLE). From there, you can use DSU/Cemuhook mode to emulate the controller as well as forward gyro information, since the controller has gyro.
Steam is also able to work with the controller, but only via USB-C. And in case if you happen to have a BlueRetro adaptor, you can daisy-chain it to a Wii U GameCube controller USB adaptor if you wish.
I have to say though, on Linux, reconnecting over BLE is quite buggy, but with a bit of determination (
usually pairing again), it works. Also, depending on whether your controller is from a newer batch, you may have to
manually edit in a MAC prefix corresponding to your controller.