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 A language you learned from your captured opponent today might be outdated four weeks from now.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.
We see the Ferengi have them in their ears. And given they can still understand each other when their comm badges are taken off for whatever reason, I'm inclined to think they're not there.