JoJo's Bizarre Adventure - Bites The Dust Is Awakened

That is what happened, but it's hard to say if it's a constant due to lack of data. It's possible that, like the shot that allows you to acquire the stand in the first place, it carries risk of death. Or, because Killer Queen has high developmental potential, it's possible that the second shot acts as a boost, unlocking what was already available through effort (for example, had Jotaro been shot before learning The World's power and realizing his own, it's possible that Star Platinum: The World would have been granted to him by the arrow)
Or it could just be that getting hit by the arrow again gives you additional abilities, like you said. We'd really need to see more stand users hit a second time

I love how it switches between Kira and Killer Queen in that one shot.