Is There Any Downside to Using An Air Impact Driver to Drive Screws?
You are talking about two very different machines. 


an air impact wrench used in shops on bolts typically 3/8" and larger, that would be too tough to work with a ratchet or breaker bar. The classic example is a tire shop removing lug nuts.
An electric drill.  It looks, walks and quacks like an electric drill.  Except it's jazzed up with a geardown for driving screws (a "drill-driver"), and a centrifugal impact feature to give it a bit more "kick" to help you cam out screws better ("impact drill-driver"). 


The tool you linked is made for electric drill-drivers.  

For your air impact wrench, the tool you're looking to break is called a bit holder. It's a much simpler affair. It snaps onto a common 1/4, 3/8 or 1/2 square drive meant for sockets, and gives you a standard 1/4” hex drive that takes Philips, Torx, Robertson etc. bits that you normally use for deck and drywall screws. It has a magnet or clip to keep the bit in place. 

I prefer using one with a speed wrench.