Not really, because the UT can always be re-tuned. A language you learned from your captured opponent today might be outdated four weeks from now.
Learning the "native" Breen or Cardassian language would not be a tactical concern, because all battlefield communications would be handled via the UT. Prisoner interrogation after surgical removal of UT would yield results in a language the interrogator can comprehend - but that's true of interrogations in all circumstances, and secondary to the tactical consideration of battlefield eavesdropping.
Did we ever see one surgically implanted? I thought the device worked through the communicator pins.