You could probably do away with the sound card. Most motherboards have onboard sound nowaways anyways, and it's usually sufficient for most people.
Would the motherboard I plan to purchase be able to lose it's soundcard without an issue?
I can't be sure, as the only information I could find after a quick google search was of the Gigabyte GA-970a-D3p, rather than the Gigabyte GA-970-D3p (not really sure if there is a difference.) However, I haven't encountered a newer motherboard that didn't have onboard sound, so you should probably be good if you omitted the sound card.