If you have a video card with a fan and computer with a fan, the computer fan usually can make noise if it is operating at the fast speed. Very noisy in fact with some, because newer computers have more to deal with, and during high activity periods, the fan will start making a lot of noise. Now with my computer I usually have it on optimal or something like that not hi-speed because for normal general computing (usually including DAW but I do not use soft synths) the fan will be quiet enough, but I found out that if I change it in the BIOS to the fastest speed, the darn thing is very noisy. For computer games that may be needed to keep the computer cool (and video card maybe not as noisy but perhaps could be) during hi-speed stressful computer use. Then a lot of people seek low-noise fans when building a computer for a DAW because the fan will be virtually noiseless even when used hi-speed. I have not needed that yet, but I know my fan in my computer will make a lot of noise if I set it in the BIOS to the max.
Also some computers nowadays have way more in the computer than I do, so the fans can make noise just having the computer on. Yes, even normal fan operation can be noisy for recording but if you have a noise gate (and the only time I have to think about it is when singing) then with my use, since singing usually does not have such a dynamic range from soft to loud passages, then the noise gate will not let the noise through below a certain level. Say a voice singing has dynamics of 50dB then a noise gate set to 60dB will not let noise get through if the recording is loud enough into the DAW without distorting the signal.
Yes, a low-noise fan would be better for any DAW actually.