Yes, if you use an asynchronous USB connection, your DAC will act as the master clock and rely on its internal clock. For other connections—such as coaxial, optical, AES/EBU (which you have), or even I²S—the clock information is embedded in the signal, and the receiving DAC must synthesize or lock onto it to reconstruct the clock. In these cases, a cleaner, lower-jitter incoming signal also helps.
I own the Harmony Micro DAC, which is one of the few DACs that allows users to choose between its local clock or the I²S clock when using I²S input. I experimented with and without a DDC. With the DAC’s local clock selected, the sound quality still improved as the DDC quality improved (I tried the SMSL and the Gustard U18), because the cleaner the input signal, the better the result.
I’m simply sharing my experience for the benefit of the group. Your mileage may vary because you have a different DAC. I suggest you try it yourself—for example, compare USB with other connections through a DDC, starting with the SMSL. The home trial is risk free, why not.