This is something I do, minus the speed. Not just my favorite song, but music in general. While singing or playing an instrument, it leads me to mimic what was recorded. Listening to different versions tends to bug me - during karaoke, for example. I’ve sometimes performed a cappella rather than change key.
Yesterday I found a few tunes I haven’t heard in twenty years, but startled myself by singing along note for note. If only there were language courses that taught vocabulary through song… 
