No technical reason it can't be done. I've seen some Porsche guys have under-car mounted trans coolers in the rear.
My concern would be protecting the heat exchanger and pipework.
The aftermarket Porsche one I've seen had the cooler mounted at 45 degrees to the road surface and a "bash plate" on the underside which could have acted as a bit of a splitter. Strong stainless mesh grill in front of it too.
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