As far as I know, a behavior like this could be achieved only in two ways.
- If the sound card itself supports it (read the card's manual), then you might be able to connect the PC Speaker pins from motherboard to some socket on the sound card.
- There may also be a setting in BIOS to enable/disable playing of system beeps through the onboard sound chip - I was surprised when I found this setting in a computer I recently built. It is however unlikely that you will find such an option for external sound cards.
Having your sound card play the BIOS beep codes etc. is hard, because at the time in question (hardware boot-up) there aren't any drivers of sound card to be loaded and used. Either BIOS supports it on onboard chip, or the sound card has a connector to connect the PC Speaker. Other than that, I don't see how could it be possible.