Even if this worked (it will not and cannot), it will only work in SOME places, whereas it will constructively ADD in others since the fan and the speaker are not co-located. To make it work in ALL places you'll need an infinite number of speakers with precise phase control for each. This is how beamforming works. Fun stuff. Mathematically quite a bit more complex than "put a BT speaker near a fan"

Why won't this work even if you could co-locate your speaker with the fan? Fan noise is neither stable in time nor as simple as a sine wave. This would need a complex active system to work.