At any point in the course do I hear Klingon language and therefore learn how to pronounce it?
The Duolingo administration decided not to provide audio for the Klingon course. The Contributors and Moderators would love to add it and Duolingo is working on a method that might allow us to do it, but at this time, we do not know when or if it will be added.
There is a Skill a little bit into the course which teaches the names of the Klingon letters and has a description of the pronunciations in the Tips & Notes, however, that skill also lacks audio. If you want to check out some ideas for learning the pronunciation, check out the thread at: https://forum.duolingo.com/comment/26605745
If you want to read about the other known issues in this course, read the post at: https://forum.duolingo.com/comment/26778885
Unfortunately, there is currently no audio in the Klingon course. I don't think there will be anytime soon, as they will most likely work for audio with real-life languages first. But! The internet is a great resource! You can definitely hear pronunciations on YouTube! :D