Yes, nvidia-settings uses a proprietary API to talk to the proprietary nvidia driver, and the driver itself will execute the modifications. There's no way of using nvidia-settings without the nvidia X driver running, which implies that X is running.
It may be possible to run the nvidia X driver without actually having it drive any output by tweaking the xorg.conf file.
You didn't explain why you don't want the X and the driver running. If the reason is that you don't need them and only want to run the CUDA applications headless without a monitor connected, then it won't hurt if you run both, and don't use any X applications, and disable the output or put it into powersavings mode. That way, no resources will be used. If there's another reason, please edit the question and explain.
Edit
CUDA resources aren't used to drive a monitor. The card consists of a number of GPU cores, RAM, a number of "heads" that treat the RAM as framebuffer and convert it into various video signals, and lots of diverse logic. When the monitor is active, the "head" part reads out the framebuffer and displays it. That doesn't use any GPU cores at all, these are only used to produce an image in the framebuffer if the card does rendering using OpenGL etc. The only drawback of having the "head" active is that it takes power, and that it needs to access the RAM, which may or may not slow down GPU RAM access somewhat depending on how the RAM is organized and how the RAM is used. But of the "head" is in DPMS power saving state, even the framebuffer is not accessed, so there's no resource usage at all.
And the same happens when you use a framebuffer driver - X is really a framebuffer driver with an ancient interface (the framebuffer interface is a lot simpler), and OpenGL thrown on top of the ancient protocol.
So, there's no need to worry.
