It has been a while since I have tried this. I tested this again and this is what I've found.
Correction Edit: One can use the REC and PLAY buttons from the UI to record a signal off the air. Then, push MOX ,then PLAY and the recorded audio will play back legibly over the air.
Under the Wave tab at the top of the UI, recording from on the air signals are possible. They can be legibly replayed if MOX is pressed. From this point the transmitted .wav file can be played and monitored via the MON button.
Rob, W1AEX uses this example in the video demonstrating how to record the transmitted signal. Then, playing it in a loop while adjusting your own settings under the Setup>DSP>CFC tab utilizing the CFC audio tools. That video is here:
https://www.youtube.com/watch?v=l5JmDAaDBVo
This is a very good video on utilizing the CFC Audio Tools. Maybe this video might help with the question asked.
I have used this method to record, by request, and playback another's audio signal on the air to give them and idea of how they sound. Even this is not straight forward or easy. From what I can tell this is the only way to record and listen to a wav file from within Thetis.
Of course, the audio file can be played from a player external to Thetis.
Maybe the original question can be answered from within this information.
I have requested ,via Want/Wish, that the Recording and Playback be looked at.
EDIT: I have edited this post so many times now that it's almost completely new.

I just want to make sure all my facts are indeed that. CORRECT
:::Content edited for spelling, grammar and lack of a good train of thought.