It depends how powerful the built-in amp is in it's power output.
@Silou seems to have
done some calculations in the DAC1 review thread as to what the power output might be, but this hasn't been confirmed by measurement, as Amir didn't test headphone output when he measured it, only the DAC section (which didn't seem to measure well).
If yours doesn't have USB input though, then it might be a different model than the one that was reviewed in this thread, since this one does in fact have USB input. If Silou's guess is right though, then it would be about the same power output as the Atom, so not really worth the upgrade.