The inertia of the fan blades rotating probably limits the data rates you can get with this method, assuming rotation speed correlates with sound frequency (to distinguish between 1 and 0). I would guess it might be a few bits/minute.
I remember reading, in a computer magazine about 15 years ago about a technology, or else an area of research that claimed to do just this. To infer what is being typed on-screen from subtle variations in radiation emitted from the monitors. Apparently some degree of success was possible even outside a building. It probably related more to the CRTs of the day, and the less noisy UIs.
"Data Exfiltration from Displayless Speakerless Air-Gapped Fanless Computers with SSDs via Subtle High Frequency Modification of USB Voltages". AKA your mouse wire is your new antenna.
You could modulate the data into an analog signal using the range of distinguishable sound frequencies from the fan and probably achieve a useful data rate. Modems do something similar to stream data over a phone line.