Can a video or audio stream recorded through FMS be played back via a regular,
non-streaming Flash file? The audio and video clips would be short and it
seems a waste of a FMS connection to stream the file when playing the clip back
in a non-streaming method would work just as well. I'd prefer to only use FMS
connections when absolutely necessary, like for recording, chatting, etc.

Yes you can, you just have to make a virtual directory on IIS or symlink on
linux to your video app directory and do not forget to activate the mine type
for the .flv flv-application/octet-stream if you use IIS.

Good luck