Most all automatic transmissions incorporate some sort of by-pass in case the cooler becomes restricted, but they are typically found inside the unit.
In either case if the thermal by pass valve is not heated when flushing, to fully stop by-passing the cooler, you will get little if any flushing of the cooler.
Here’s another thing to consider. If the cooler is plugged and there is a mechanical or thermal mechanical by-pass in the lines you’re flushing, it will by-pass the cooler. In which case there would still be flow, but would not have sufficient cooling. If your cooler flusher has a pressure gauge, it should indicate higher then normal cooler pressure if the cooler is restricted.