Any gap between exposures beyond a few seconds will show gaps in the startrails. Skip the long exposure noise reduction and shoot a dark frame to use with the Startrails program. That will eliminate noise very effectively.
Concerning use of long exposure noise reduction, yes you can put a lens cap on the camera and move it while it is shooting the dark frame. But, you must keep the camera in a like temperature environment while it is doing it. If you move it to a warmer environment it changes the sensor noise patterns and will be ineffective.
Tom From Beautiful Smith Mountain Lake in Virginia