Yes.
This was the first time a lot of people realized that there is a way, other than war, to rapidly advance science, knowledge and technology. It was the first time we set ourselves a massive challenge without actually being at war, although the Soviet Union's surge ahead of us technologically definitely, at the time, had serious implications. You kinda had to be there, but remember, these were the two nations that emerged stronger from WWII, and they represented diametrically opposed paradigms of what life is about, how humans should be organized, what humans actually are. There was an ongoing, aggressive struggle from both to dominate. And there was indeed a lot of residual patriotism lying about: Both the Soviet Union and the United States had to reach deep into emotionally driven patriotism to triumph in WWII. A latent pool of that emotionalism was still available, and both sides tapped into its energy.
More sophisticated people analyzed it accurately then and now, but the point is: Because of NASA we all know we don't need the impetus of a life and death struggle to stimulate creativity and originality. We do need something massive and bigger than us, an environment that not only encourages those traits but is willing to embrace and deploy the results. A huge effort in support of, essentially, the more positive human traits like curiosity, pursuit of discovery, even simple wanderlust, is much preferable, in my mind, to a huge effort stimulated by fear of extinction at the hands of a rival political philosophy.
If you take the essence of NASA and project it forward, you get "Star Trek," whose mission statement is discovery, not domination. That's just an indication that even in the world of television and movie entertainment, the meme was moving along.
That can't be all bad.