I have an excerpt from a HMI book with references to papers that claim that auditory feedback can lead to increased typing speed. That does not prove the converse, however: that a completely silent keyboard would be detrimental. Tactile feedback would provide the same effect for a keyboard that is otherwise relatively silent (or unheard: study participants wore headphones with white noise).
The studies do also say that feedback must occur immediately after actuation, otherwise it will have no effect. A study tested with a consistent delay to the click sound: after a certain time, a group of more experienced typists had learned to adjust to the click being delayed, while a group of less experienced typists did not.
I suspect also that if a keyboard is too rattly, clicks on the upstroke and/or is very loud on bottoming out or topping up, then the auditory feedback could gets lost among all the other noise, thus reducing its impact. All my keyboards with Cherry MX Blue have O-rings for sound damping for that reason. It sounds better to my ears if I get click without the clack.
BTW. I do think that I myself do inhibit my typing a bit if I feel that the keyboard I use is too loud and harsh — that it sounds like it would break if I type on it too violently. I have got that feeling with some keyboards with MX Red, where I would bottom out easily and feel it.
Heh. Imagine a keyboard that would provide an auditory crunch if you bottomed out, but only sometimes: how horrible that would be.