Can a filter circuit be built for the FM broadcast range to only pass the frequencies not bearing a broadcast stream?
Of course it can. What you need to do is to perform a band scan and look at signal strengths. If you plot it, you would get something like this:



If the signal is above a certain threshold, some station is broadcasting on it and you can skip that frequency. If the signal is low, output it to the speakers.

Now on how to implement it. My approach would be to use one of the off-the-shelf FM receiver chips (e.g. ​Si4702) and a small micro to drive it. That's about all you need these days!

Watch out for any processing (the Si4702 has "Adaptive noise suppression"), which may interfere with what you are doing. Do your own research and pick a chip that suits your needs.