I have had a Mercenary since beta and launch, so I feel a little silly asking this question. Has rapid shots always worked on self? I could have sworn it didn't work on me at one time, though It may be that I didn't really notice due to the lack of sound.
As for adding a sound to it...YES please!! While it isn't absolutely necessary, it certainly does help to stay in the timing rhythm. When I have tried healing others without sound in the past, I was definitely thrown off my game a little so I have no doubt it will do the same when I heal myself with it.