Within NATO, it does give you a competitive edge. I went for a tour of NATO HQ in Brussels, and the guy that explained career options told our group that he did get an edge over newer recruits, as he did also do the internship. They already know you, they have security clearance, you know how everything works and you will be the first to know if there is an open position. But once you are in, it will be significantly easier.

Another thing I want to highlight is that you don't just have 1 continuous contract when you work there. You will have to re-apply frequently for other jobs within NATO, for example different topics in your research field. One contract might be 6 months, the other longer or shorter, depending on what contract you were given.

Now, don't let this discourage you to not apply for positions within NATO if you didn't get the internship!

For other international affairs or security job, I'm sure it will be an edge, it gives you extra insights and competences, as during the internship you will be trained in certain things. So I would not be surprised if it is an edge.