what you're talking about would have no performance gain, more than likely a performance loss, and a higher cab tempterature.
something that does work, which a lot of the gen 2 Lightning guys are a fan of, is what's called a Killer Chiller.
those trucks utilize a water-air intercooler core, located below the supercharger (roots or twin screw type) in the valley of the motor, inside the lower intake manifold.
Stock, an electric pump, pumps water through that intercooler core, and into a heat exchanger (think small radiator) behind the front bumper to cool the water back off before it goes back to the intercooler.
The Killer Chiller uses the A/C system to cool the water itself, allowing it to reach below ambient temperatures before it goes back through the intercooler underneath the supercharger.
Just adding the Killer Chiller to the stock system, usually results in lower air temperatures post supercharger than the guys that run bigger single pass intercoolers, bigger lines, bigger resevoirs, and bigger heat exchangers. It works pretty good.
For a PSD, the only way I can see that type of setup working, is instead of adding a big air-air intercooler behind the grill like we all do, is to use a water-air intercooler located wherever you like, with that water being run through a heat exchanger and a Killer Chiller setup. Although there is no bolt-in anything like that made for these trucks, it would all have to be custom made.