I built something like this years ago. I used plywood to create an external box with fans and an automotive grade air filter. A 4-inch diameter tube carried the clean air into the PC. It worked, but it was loud and not very portable. The trick is to pressurize the inside of the case with clean air, meaning that the input of clean air must be higher CFM than the fans blowing out of the case. If input < output, then dirty air will get sucked into the case through crevices, creating dust clumps. If you can't pressurize the inside of the case with clean air, then you need to design a case that is air-tight so that all incoming air is forced through the air filter, and not seeping in through some unfiltered slit in the 5.25" bay.
It was during this project that I learned about concepts not mentioned here in this article: "Static Pressure" as measured in in/H2O or mm/H2O, fan noise as measured at different flow rates (Cubic Feet per Minute through a restriction), and fans vs blowers vs impellers. Generally speaking, at the same volume (decibels), a blower (squirrel cage fan, or centrifugal fan) will generate a higher static pressure than a standard fan. Meaning, a blower can pull the more air through a filter than a standard fan at the same volume. The problem is that blowers turn the air output 90 degrees, whereas a standard fan blows straight through. Video cards use blowers all the time, but I've never seen a computer case that incorporated a blower.
If you want to get the same static pressure out of a traditional fan as compared to a blower, then you need to raise the RPMs to some unbelievably high number. At this point, you should be thinking about those three-bladed Delta fans that shriek like banshees. Nobody wants one of those a computer case sitting three feet from them.
I would like to see this case first hand.