I'm no trans expert, but would recommend that based on my personal experience with my T-type. A trans temp gauge is a good investment to moniter this. My trans runs between 165 to 180 with a n/l 9" conv, which is good, and usually 20 degrees less than the radiator temp.
If you have a REAL trans cooler on the front and not one of the cheap parts store specials then you should be ok without the in tank cooler. However, if there is nothing wrong with the cooler in the radiator you might as well leave it hooked up. Liquid/liquid coolers are very efficient and if you run it through the stock cooler first, then out front to the AUX cooler, the trans temp will stay below coolant temp AND will allow proper temp to be reached quickly in the cold. In the summer, the fluid going into the radiator will be very hot and the stock cooler will get the fluid temp down very close to the coolant temp, and the aux cooler will knock a few degrees off of that. Keeping coolant temps in check goes a long way toward keeping everything else happy.