Is it the plastic tank that cracked? I have seen that more than once, plastic does get brittle over time from repeated hot/cold cycles.
One other thing to check; make damn sure you do not have a head gasket starting to go. my nephew just had this on his 02 Grand Cherokee, (4.0) compression is much more than rad system pressure, and radiators are only built to handle what is listed on the radiator cap, engine compression can be 8X that.... so that'll find the weak spot real quick.
I have his engine apart and at a machine shop as we speak, as a result of the blown head gasket (he ran it too long like that, melted several pistons too/ nother story)
To answer your original Q, no, unless they cracked the tank wrenching the fittings loose from the trans cooler within the radiator, no, removing it from the loop will not cause (radiator) failure. If that were the case they would have noticed the leak "right away" and you'd have gotten another phone call while they still had it in the shop, if you get what I mean.....
I know that many transmission shops will do as they did to yours as a sort of "standard procedure" when a major trans failure happens as the burnt up clutches circulate thru the system and settle throughout, sometimes clogging the included transmission cooler. This would lead to a repeat failure-fast. I personally flush (and utilize) the original radiator-trans cooler within the system. If I find one clogged, I may add another cooler but I also replace the radiator. I have never had luck with a trans lasting very long on "just" an external cooler by itself. I would want to add in a trans temp gauge
("t" it into one of the cooler lines) to keep an eye on fluid temp. Anything over 200* is definitely bad for the trans.... (and coolant temp does not necessarily equal trans fluid temp)