Yes—generally you can move the camera while Long Exposure NR is running, because the shutter is closed during the dark-frame capture, so camera movement will not blur or change the recorded image.

The main thing to avoid is changing the camera’s temperature significantly during that time. Long-exposure noise depends heavily on sensor temperature, so the dark frame works best if conditions stay similar to the original shot. Reframing on a tripod or moving the camera slightly is usually fine. But moving it from sun to shade, shade to sun, or from cold outdoor air into a warm coat or indoors could reduce the effectiveness of the noise reduction.

So: position does not matter much, but keeping temperature conditions similar does.