I'm pretty sure my first computer(E5200) has a connection to connect the graphics card audio jack to motherboard. I've looked at it, but it doesn't seem like it will fit the wire that was provided by the graphics card manufacturer(Nvidia GTX 260.
My second computer is a little older. I don't see any audio jacks on the motherboard. The Geforce 9500gt does have a HDMI audio option on the card though.
No. Hdmi input is a special port shaped like an oddball rectangle with 6 sides. To select a motherboard, use newegg's software under advanced settings to narrow it down, even if you don't buy from them. Select "hdmi support" as one of the search settings. Hdmi ports can also be found on some video cards selling for around $60.