Yes it can. There is a high pressure line and a return line both at the bottom of the radiator. Most likely you will need to get on your back with a flashlight and look up. Most of the time the lines are metal, sometimes the return line is rubber about 3/4" in dia. Check where lines attach to radiator. What you are looking for is leaking fluid. GENTLY tighten the fitting. The radiator is most likely plastic so don't do more damage by ruining it! Also wipe the lines clean and look for cracks or a break in a metal line. Follow the metal line to see if it touches other metal parts or the chassis. This contact over time can wear a hole in the line. A temp fix is splicing rubber hose for high pressure applications where the hole is. Cut line cleanly, slip the right size hose over [you may need to buy several to get the right dia but you only need 6 inches] and use small hose clamps, slide one side then the other on, secure it w/clamps. Start car, observe. Test drive. Observe. Or your plastic radiator may be cracked.

Causes of abraded metal lines could be bad motor mount allow engine/trans to move or sag etc. So also look for the root cause as the lines as designed don't touch metal parts. As soon as possible purchase a replacement line, the hose patch won't last forever.

Absolutely! 99% of cars and trucks have the automatic transmission cooler inside the left end tank of the radiator, facing the engine with the hood up. The dealer of your car can pressure test the cooler to see if it's leaking automatic transmission fluid inside the radiator.

transmission cooler lines run from radiator to transmission so if one of those lines leak then you'll loose transmission fluid. find local shop at ATRA.COM for more info

Some radiators have a transmission fluid line connected to it .