The dust won't damage anything - except as I will explain later. You can also always clean the dust off. The risk of causing electrical faults is probably much greater - things can get in there and mess up. fingers - cats, cockroaches - you name it. They can get in the fans or short out a part of the circuitry.
TH excess dust can interfere with cooling though. It acts as an insulator and prevents the transfer of heat to the air, so the components get hotter and things like the fans and heatsinks get less effective.
A better solution is to get fans with filters or the intakes and then close the case up and move the air in a directed fashion over all the components.