Good thread topic.
I chuckle every time this movement makes the news. What started out as a misfit band of Che-inspired, violent dictators in populist clothing...has remained exactly that after 50+ years!
NAM provides no valuable benefit to the world. In fact, it harms the planet by lending legitimacy to the useless regimes that often end up setting its agenda. What's worse than the UN? The UN with only the lamest countries involved.
All of this said, the unfortunate answer to the question is yes - they do have an influence on world events. It's simply by virtue of the time and money spent by these countries on their futile initiatives.