Is it possible to run Transmission coolant line outside of the radiator? on 1997 Mercedes-Benz E420

Recently i had a problems with my Transmission box. Coolant system had leakage, and antifreeze mixed with water leaked into transmission in result mixed with transmission oil. As the result of that i got my Torque converter stuck. I bought used one. Now transmission is ok with a working torque converter. But i don't wanna start the engine untill the leaking is fixed. I would like to know, if there is any possibility for damage of my transmission if i'll run coolant tubing (that goes inside the radiator) outside?

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