The video card doesnt produce sound, you need to pass the sound through the video card via a SPDIF out cable that connects from the SPDIF out connector on the motherboard to the video card. Most modern video card have the passthrough integrated already so you dont need such cable and if you do then the cable should be included in the box.
A sound card is far better than onboard sound. If your building a HTPC a sound card is not a hassle at all and they're innexpensive. Yes, it is better to have a current video card, but for your needs you're better off with a video card that meets your needs and a sound card. I recommended you a budget solution.