Yeah. It's implied the natives not only see the Enterprise, but probably believe it saved them. It could become a story in their culture, or even part of a religion. But would it have a lasting effect on their development? That's problematic.
That said. It's always seemed to me that Kirk lived by the mantra, "It's easier to apologize than to get permission." Whether or not Kirk would be punished, he'd stick by what he did, not cover it up, and say to Pike, "Gee sir. You're right. I should be punished, because it's far better to let a few million people on a planet die from a catastrophe that we can prevent than it is to 'pollute' their culture simply because they're unfortunate enough to be pre-warp and see a UFO. Yes, sir. I can see why it was so much better to just watch these people become extinct. We don't want to be God. Better to let them die than intervene however clandestine. Oh, wait. Letting them die, that's being God, too, isn't it, sir? Oh, well, I stand by what I did and accept my punishment."
That's more like Kirk, and better than lying about it from the start. That seems soooo out of character.
Further, what ever happened to courts martial? Doesn't Kirk get due process before being relieved of command and demoted? There was a hearing about cheating on the K-M test. Or did he wave due process and admit he lied in his log?
According to Google, one translation of "putaquepariu" is "holy shit!" "Putaquepariu!" indeed.