In the case of the DS doing a conversion from PCM to DSD outside the DAC probably isn’t going to do better than letting the DS do it. 1) Conversions from PCM to DSD are even less well defined that PCM upsampling (and we know that there are a lot of different sounding upsamplers out there.) 2) A PCM to DSD conversion involves a sigma delta modulator and doing one modulation outside the box and another inside the DS isn’t optimal (tho not necessarily lossy in the sense that you might have meant.)
A good sigma delta modulator adds less noise in the audio frequency band than doing 24 bit dithering - that’s not really an issue. Doing a DSD conversion at at least 128FS doesn’t need to add significant noise above the audio band that won’t be filtered out by any DSD dac downstream…