Um, no computer generates dust.
I guess you mean will it collect dust, for instance on the CPU heat sink.
The answer is yes, but much more slowly than you're used to. If you have pets in the house, you should still blow out your system about once a year, even if it doesn't have any fans.
a computer can do alot of things, electron is in the word electronics. from the second it is started, it is ionizing. ..and that is a good one.
there is always an opening somewhere that can gain the ionization. some have cases mastered, some inspect motherboards before thier first run, finding solder openings a bit too much to leave open...these things help stop dust.
with this ionization ability, spaghetti water boiling in another room can pass zinc from one end of the unpainted spots of a SECC pc to another...whenever it feels like it...that is called electroplating, of course the mosfet(s) lose after awhile. 3-5 years is doing darn good. that is the most complex dust collector in the pc world...the very case it is sitting in could be exactly wrong.
positives flying meet negatives grounding, the pc has alot of grounding...
heatsinks in the psu are very lively to the wall outlet voltage, that is a place that pretends
its all good as well....
the brown crud could be parts of YOU building up in the fans...
the only way to avoid a dusty pc is unplug everything, put the mobo in a bag and take the battery out too...then it is stopped and silent. And ya know, there is no such thing as a silent pc. there is a clock at 14.3 MEGA hertz for good ear listening "pleasure"...some like alot of fans just to drown that high pitched squeal. I hear it...it goes with my 20/10 vision. I must be blessed to give the pc hell...
not to mention all the collisions to get the theoretical megahertz we all throw our old stuff out for, ya know getting faster and faster all the time, we must have those big big numbers.
Optimistically, electronics can be built correctly, it seems the third world country creating it needs a kick in the ass first.
I do have several electronic devices , completely sealed, and write to memory, and read...completely sealed. Knowing this only proves, all motherboards are experiments temporary for us to play with, they are NOT seriously built or thought out, including the ever crazy power supply we can breathe through and stick little fingers in....
add filters, create intentional grounds .I use aluminum fine mesh in front of a front fan..big big helper for the rest of the case- it delays cleaning by months of runtime. The hdds can be blocked off if in a thermally good case for your system, it will use the thermal value of its surroundings to stay cool...if hopelessly stuck open in front of them, seek SECC painted or even the EMI B rated metal from an old floppy to stop the vents, or slow them down. the hdd is a big grounder, hence ionizer, hence dust crud and even smelly acid.
that is as far as I have gotten with an extreme system.