I work at a coal-fired power plant. Coal dust, fly ash, dust off the roads, etc. is continuous here. We leave the PC's on all the time. I've opened some of them up and I guarantee you that keeping them running does not protect you from dust accumulation. The ones I looked inside were black. The parts could not be identified except by their general shapes.
I've been thinking about how to protect our most exposed PC's. I think the only thing to do is build a large box around them, then bring the monitor/keyboard/mouse cables outside the boxes. I'd build a plenum where a standard HVAC filter would slide in, and install a couple of 120VAC 120mm fans behind the filter to keep the box pressurized. I'd build the intake down low on the box, and build an air outlet behind the PC's. You'd have to run some temp monitoring utility, like Speedfan, to make sure the PC's weren't overheating.
We have some big fancy PC consoles that were bought from commercial computer office suppliers. The PC's are situated down low inside the cabinetry, and the monitors are perched inside some hoods with glass windows. These consoles have fans, but no filtering systems. The PC's inside are just as filthy as the ones sitting out on the counters.