The data stored on the HD would be identical to the data on a music CD, but transporting this data to the DAC would result in the same problem as transporting the data from a standard CD transport to a DAC. It's also a one-time process that results in jitter, RF interference and etc. In a computer environment, it would be quite bad.
Also getting an exact copy of the digital output is not quite easy. For example, in a Windows XP environement, XP's sound mixer SW will resample 44.1kHz to 48kHz and back again at the sound card. This will result in errors. For bit perfect, need to bypass the sound SW with Kernel streaming or ASIO SW and make sure that the sound card used does not resample as well. (Most SoundBlaster resamples) This problem is a legacy problem. Early cheap sound card only process everything at 48kHz to save money. So all sound data are re-sampled to 48kHz to save time.
Theoretically, computer should be a much better transport by a long shot, but it's not quite as easy to use IMHO.