I don’t know about harm or no harm but for sure the air pump will work harder because of the added static pressure If after cooler is between the compressor and the tank.
Also depending on where you locate your check valve you’ll be losing more air cycle . When that section of tubing potentially including the after cooler unloads in preparation for the next ON cycle.
You’re also subjecting you’re after cooler too far more vibration. Between the pump and tank.
And a vast majority of these installations people are using a oil to air heat exchanger for an application that should use an air to air heat exchanger. I find that course of logic really odd.
If you really believe that you wouldn’t be on here every single day trying to help people do it the best way.