The DAC-1 has a built in AC transformer, which would be something you'd want to bypass, unless you feel like using a DC->AC->DC path, which would probably be inefficient.
Also, the DAC-1 runs pretty warm in idle mode, in fact it seems just as warm as when powering headphones. I wonder if it runs biased in Class A.
Remember, it's not just a DAC, its got an amp section. It won't be as efficient as the DACs that are designed to run on battery power.