The idea is that the languages that get added are part vocal/auditory, part non-auditory. So you in your example, the officer would still hear them, but not understand them. Not sure if it's possible, but if they would understand pidgin at least, maybe they understand half of it, or get it translated into some misleading/senseless sentence, as the character hears the words, and tries to make some sense into it. It wouldn't be that much different talking local as it is currently with the existing languages.
About more species specific language on comms, this would do nothing, as the headsets only transmit the auditory signal, and such, half of the message would not be understandable: "** code sh** **ble l** th*", which was "The code should scramble like this", manually scrambled.
About the vox getting this telepathy, for which they also need to shriek to utilize it, i figured that would be a lore fitting explanation of how they would have a non-verbal component, rather than giving vox, taj, vulp, and unathi tail movement as non-verbal component.