Does this app synthesize a new song everytime it alarms you? Not exactly clear how it works from the playstore description.
No, all the phones will pull the data at a different time, so it should keep the load down from the server. Plus there is a bit of randomness thrown in for good measure.
It doesn't actually fall back to the last song. It caches the current song, but if for some reason the cache doesn't save for some reason. Or if you are offline. Your phone's default ringtone will play.