Most graphics cards with HDMI connection can out put sound over HDMI, i think there are some Nvidia ones that can't but think there is a chart on the Nvidia site that lists the features of all their current cards.
What are you trying to improve with a separate graphics card, if all you want to do is play back blue-ray movies (either rips or the physical disks) then the integrated graphics on he i3 will be fine.
I'm not sure about 3d play back with the i3 but have no issues with using my AMD A8 5600k playing back 3d movies using TMT6.
If you want to get one to improve game performance then yes a good quality (expensive) separate graphics card will be better but you then will have to think about a bigger power supply and maybe improved cooling and with that then comes noise. Regards Aquatarkus