This is a good idea although... I would recommend simply adding the transmission cooler inline with the one already in the radiator. I am a transmission tech and to tell you the truth, the scenario you describe is one I just don't see very often. Overheated transmission fluid though, I see as a cause of major repairs consistently.

Hook the new add on cooler up in line before the radiator. This way, in the winter, the fluid can be rewarmed a little if needed by the radiator cooler. This, (fluid being too cold), is as far as I know, only a problem in the coldest most northern most climates.

In the summer time, it may be possible to cool the transmission fluid cooler than the radiator thereby acting as a small heat transfer to help maintain a cooler radiator temp. This should all still provide a reasonably cooled transmission fluid back to the sump. It will be dramatically cooled from the time it left the transmission on it's journey, and you won't be adding any or as much heat to the radiator and could possibly remove some. You shouldn't overlook the potential for cooling that exists along the transmission lines on their way back to the sump either.

The transmission and coolant both have temp sensors and I would suspect that keeping the temps somewhat relative would keep the computer happy as well. Though I am not sure what the computer strategy is based on the input of these two sensors together, or if there is any at all.

Either way, it should be beneficial. I wouldn't completely bypass the original cooler unless it was stopped up from previous transmission failure. If you don't keep the trans cool enough you will definitely have problems. Heat is the #1 enemy of automatic transmissions of any brand.