Tranny fluid running through the coolant passages won't hurt anything. It's the coolant running through the tranny that's an issue. If the trans was indeed replaced it's fine. That's no reason to avoid it.
If and only if the radiator was replaced and the engine coolant was flushed.
__________________ '13 Tacoma TRD-OR: The Spruce Goose. BUILD '02 Sport Ed.- V2.0: The better build. TotaledBUILD 2.0 '02 Sport Ed.- V1.0: The college build SoldBUILD