You'd certainly have to fit a transmission oil cooler at the very least.
Automatics stand up to the torque of modern turbo diesel engines so I can't see that there will be a problem in principle. Autos have been used in all sorts of engine configurations for years from the tiniest 1.0 Micra to the insane Audi Q7 with its mighty V12 diesel.
I'm slightly surprised by the question to be honest. It's kind of like asking would it be OK to have a two door car with a blue leather interior?