Given that DACs contain an analog section, it's pretty clear that they can indeed sound quite different, if that's the intent of the designer. I mean you can tweak, or even omit, the reconstruction filter if you like the way out of band aliasing sounds.Wouldn't be the first time.
The question is, do you want one that *has* a distinct sound of it's own? Or one with the most accurate reproduction? The former will be a form of fixed tone control you may not want if you're an equipment junkie and change components frequently. Maybe it fits with the next gear iteration, maybe not. This type of "voicing" is one likely culprit for what I consider to be the "system synergy" canard.
Whichever floats your boat.