Is it possible to display an indication that audio is playing in Keynote?
Here are 2 possible solutions:

Make the placed audio icon larger then std (53x53 pixel), then move your mouse into that larger region while in presentation playback mode. (The controller is not visible while editing your presentation.)

As with the standard-sized icon, though, this icon will not appear in presentation mode. 

To access the audio playback controls while in presentation mode, just move your mouse into the region of the large icon (up to 400 pixel), and the controller will appear.

NOTE: it will require mouse controls during presentation so I prefer the second solution.

Second solution:
There is a possible way, and I think it is the ultimate way to do it:

I would create a video template with something like spinning wheel.

Then I would add your music to the video, and repeat that as many times as you like saving the video each time.

Now you will be inserting video files that are actually meant only to play sounds while showing a little inconspicuous rotating wheel for your information when that file is running.

I would recommend to leave the first and the last video frames empty so the do not show when sound is not playing

Since it is really not a video you are watching you can size it to what ever size you want.