Why you should get more noise?
Instead of getting an overexposed picture with for example 1/60 shutter you get a right exposed picture.
Same ISO, same shutter no underexposed picture -> not more noise
Shure, theoretically with high light and high shutter speed you would get even less noise but that´s not noticeably.
No camera is noisy with iso 100 and 1/60 shutter.
I shot all my anafi videos with ND Filter an 1/60 shutter (or 1/50 when filming 24fps) - no noise correction needed.
Shure, the anafi is not great performing at low light, but thats another story. Has nothing to do with daylight filming and getting 360° shutter with ND filter.
One important thing with ND-filters is that you should get good ones.
Where cheap ND-filters can negatively effect the image quality are the colors and maybe the optical quality of the glass.