I doubt it. If you're thinking of the large electrolytic caps in photo flashes, it's an oscillating transistor/transformer that causes the whine. The oscillation is used so that pseudo-AC voltage is created from the batteries, allowing the transformer to boost the voltage enough to fire the flash.
AFAIK, there are no electrolytic capacitors, transformers, or transistor-oscillating circuits on an ODAC and there shouldn't be anything that would cause oscillation, either - except the clock chip. I don't know enough about it and haven't heard a DAC that does this - but I would suspect something in the clock or USB negotiation that causes it.
If thats the case its very odd, because acc. to the post the whine is external, not through the headphone.