To be clear, James means the oil will go from the pan, up the pickup tube, into the pump, then to your cooler, then through the filter (or filter than cooler, depends on the adapter), and finally to the engine.
The "return" from the engine is just going out of bearings, through the oil squirters, and running back down from the valvetrain. Trying to capture/cool this oil isn't practical.
You do not want to put the cooler on the suction side of the pump. The less distance the oil has to travel from the pan to the pump, the quicker it will prime on startup, and the less places to leak/fail you have.