You could say that if you want, but that doesn't mean you're right. The exact mechanics of how Saiyan Power works has never been fully explained by the series. So there's no way to know if you're right or not.
That's his point. Black didn't wish to be immortal because he wanted the Saiyan powerups instead. But if recovering is what actually grants the powerup, then he could have wished to be immortal, and gotten both. Since Immortal Zamasu still seems to take injuries, he just instantly recovers from them.