The original Wavebird is not Bluetooth, so either:
1- this 3rd party controller is a generic Bluetooth controller that is, obviously by absolute coincidence and not an attempt to exploit Nintendo's design, in the shape of a Gamecube one - won't work without custom drivers (= maybe someone will implement it in Nintendont and emulators)
2- it's not a bluetooth controller at all (so many keyboard and mice with their proprietary usb receiver are falsely advertised as bluetooth)
3- it is bluetooth and comes with a receiver that decodes it to actual Gamecube controller signals (comparably to those Mayflash, Chronusmax, etc products)
For (2) and (3), all depends on how accurate its output is, compared to a real wired GC controller (for maximum compatibility) or real Wavebird