So it could be possible if the cancelling came from the source of the wave, such as making the spinning fan or its enclosure the speaker?
I guess the 'fan as the noise cancelling speaker' idea could be reworded as 'a fan with active stabilization that doesn't vibrate', making no mechanical noise.
A friend with a recording studio solved their problem by putting the fan at the end of a length of ducting with a couple of 90 degree bends, lined with foam.
Yes. I believe this is used in some high-end applications. It's really hard though. You need a near-perfect model of what the sound will be slightly in advance. I doubt a fan would be amendable to that.