The app itself does not, but you gotta watch out for what you use because stuff like recording, RTX HDR, radiance, filters, and more, do have a performance impact and using many of them at once can significantly affect system performance.
I turn everything off for the simple fact that it is eaier to troubleshot for a problem when you have less possible causes, and in the past, when i researched for some games, nvidia app and overlays were definitely listed as possible causes, even if it is rare.
I've seen at least one time that the Nvidia overlay caused an issue when I was playing a VR game. I've already forgotten which game it was. But I turned off the overlay.
Also I remember Pragmata crashing at the home base upgrade menu and diabling the overlay fixed it.
I wonder if that got fixed in one of the updates.