Well, they didn't wait very long to find out. Sakura began to heal him immediately. I mean, if your skin gets damaged like that, it's not a matter of a few days in any case. Maybe Naruto would have healed in a couple of days if left unattended. But since they intend to follow Oro, they don't have time to waste.

I also wonder if it was a wise decision not to tell Naruto anything. If he knows nothing, the next meeting with Oro will end up identically to this one. If he knew, though, that he became a mindless beast who attacked even Sakura, he might fight back and only use three tails. But now he thinks Oro knocked him unconscious, so he will be all the more angry and pissed off at the next meeting. Who knows, maybe enough to sprout the fifth tail. And then a real hell will break loose.