for a fighter jet with a remote pilot, you're looking potentially hundreds of miles of range, and the latency of the video transmission to the pilot combined with the latency of the controls signal back to the plane. i can't imagine that being acceptable for any sort of dogfighting scenario.
Buffering audio is actually a great answer to disconnections. Plus, it's less energy-intensive to fill the buffers at once than to stream it as needed. And since it's pre-recorded anyway, you already have the whole buffer. Yes, initial transfer can take a while, though.
But in theory, the play/pause operations shouldn't have latency, and the bluetooth device could clearly communicate its state. I'm not sure how audio is actually implemented in the bluetooth stack, though, I've only ever done serial communication with it.