Yes, they can and will affect the torque converter. Any time a transmission has a failure like that where there are bits and pieces of bearing/bushing/clutch material present, everything in contact with the transmission oil should be considered contaminated. Torque converter, oil cooler lines, and the coolers themselves are now full of metal shavings which will go back into the replacement transmission and cause it to fail.

Junk that old converter, or give it up for a core charge on a new or rebuilt one.

Did you flush the cooler lines before installing the new transmission?

Ford recommends that the actual cooler(s) themselves be replaced, which for the radiator cooler means replacing the radiator. I know some folks try to flush them but you have to be absolutely certain to get all the old junk out. If it were me, before I even connected the cooler lines to the new trans I would have flushed the lines out, bypassed the radiator cooler, and installed a new heavy duty cooler behind the grill.