I have a 700r4 that runs trhough the cooler in the radiator then a cooler in front. It's a nice setup for if you do any kind of loading on the transmission (towing, moving heavy stuff in the bed).
Won't cause any problems, just make sure the flow is going through the radiator first then the cooler before back to the transmission. The cooler is more efficient that the radiator, thus if you rand through the cooler then through the radiator, you would be heating the fluid back up a little. Still wouldn't cause an issue, just less efficient.