Yeah, in digital mode, the drive is actually RIPPING the audio tracks to the computer through the IDE interface, so you should be able to listen to the audio through your sound card.
In analog mode, the drive works as a normal CD player and plays the sound through the drive's audio out connector to the analog audio-in connector on the sound card. You should hear this on your computer speakers as long as you have the thin audio cable connecting your drive to the sound card. If you didn't connect this cable you won't hear it on the speakers but you will if you plug your headphones into the jack on the drive, and it will be controlled by the volume control on the drive.
The analog mode of the drive produces inferior sound since the D/A circuitry in these drives is pretty simple and cheap. It's much better to use the digital mode and listen through your sound card. Of course if you don't have a headphone jack, you would need to hook up your card to an amplifier that does, like your home audio system.
Hope this helps, let us know.