Disclaimer: I am not all that familiar with DSD though I have a good understanding of sampling theory (and application -- made a career of it) and various data converter architectures. I am analog guy, nothing is black and white, all shades of grey (and other colors since we are talking about noise), so I could be completely out to lunch. We have WBF experts who know way more about audio data conversion than I.
It's complicated, thus I qualified my answer a bit...
Quantization noise would be spread over a wider bandwidth and if filtered then in-band noise would be reduced. However, the analog circuits must have higher bandwidth to deal with the higher sampling rate and all that it entails (such as switching transients and such), and that higher bandwidth potentially translates to higher noise which is passed on to the rest of the system. How much additional noise depends upon how the actual DSD signal is processed (filtered) and the final circuit implementation. My assumption is that higher rates lead to wider output bandwidth (otherwise why bother?) If the final bandwidth is the same, then any intermediate analog stages must have higher bandwidth, but if it filtered ("decimated") entirely in the digital domain so analog bandwidth is the same then your argument is valid. If not, which is my understanding, and output (analog) bandwidth increases with increasing DSD rates, then more noise is output and over a broader band (note higher currents needed to achieve higher bandwidth lead to greater noise at all frequencies). How the noise is handled and its impact depends upon the bandwidth of the rest of the system.
Higher sampling rates mean circuits have to settle faster to maintain high linearity, ands that means more noise (and power). A data converter's performance (primarily distortion, which includes both harmonic and nonharmonic spurs) is often better when the sampling rate is lowered a little from its maximum value and internal (and external) nodes have more time to settle. There are also inevitably switching glitches from transistors that are worse as speeds go up, though technically you could use a completely passive filter to process a DSD signal. Of course you then have to worry about ringing the filter could introduce...
Hopefully all that babble helps a little. - Don