I don't think so.
The vibrating material is waterproof and dustproof, and AirJet already has functioning dust filters for the individual cooling units, down to one micron.
Here is your problem, you need clean air for the thing to work reliably. You need to carefully clean the air before it enters the unit.
You do not have any special air quality requirements for normal heatsinks, and when they get dusty, just suck the dust out with a vacuum cleaner.
Companies are hungry for any competitive advantages and are constantly testing and searching for them. They must have already tested air jets and found them not performing well enough, not reliable enough or too expensive. It really does not matter which one of these three reasons was the most important.
THIS DEBATE DOES NOT BELONG HERE.