Best DACs are limited by analog noise floor and digital noise floor is well below the analog one, so the noise floor is purely defined by the analog output section. In such cases the analog section would need to have something wrong to have noise floor modulation. Sometimes it can happen though, but in those cases it is primarily problem in the analog output section.
One thing to note about such measurements though, is that you may accidentally trigger "noise floor modulation" that is not actually noise floor modulation. This is because DACs usually have output mute. And most DACs also have zero signal detection, so for example sending all 0's PCM input, or any of the simple DSD silence patterns triggers this. For example ESS specifies (IIRC) that the output is muted when there are 256 consecutive bytes of same input data. This also makes it DC-block.
So in order to correctly measure this, you need to use properly dithered silence for PCM and properly modulated silence for DSD. This avoids DAC engaging it's output mute function.