Would a dedicated video card with hdmi output actually send sound out

Hi,
I am playing with different options to get better sound out of my HTPC
Everything is onbard an hdmi equipped Asus m/b, I am generally satisfied by the video output but the soundis a big no-no; horrible static through hdmi (a major flaw of this board)
For now, I have installed a dedicated sound card (I had laying around) with optical audio out to my receiver, its ok but only a temporary solution as far as i'm concerned

I could replace the m/b altogether with another hdmi equipped without any reported issues, but while looking for computer components deals, I might have came across a simpler solution
If I install a dedicated video card with hdmi connection, I might get decent sound of it, as opposed to sound from my flawed m/b

So my question is: If I just pop-in this hdmi fitted video card in there, should I get any sound out of it "automatically"?
I mean, is the videocard pci-e connection to m/b sufficient to grab the audio from the computer, or do I need some sort of additionnal connection to do that?

Hopefully my question makes sense to you

OK, then, the next question is:
could those horrible statics I was getting with the m/b's hdmi ouput come out just the same out of the separate video card as well?

Do I need to try it to know for sure; it would suck to buy & install it & endup back at square one, as the store should replace an opened packaged "doa" but I doubt they would refund

For now, I have optical out from a SB X-Fi & sound output is clean

All is well, sound coming through hdmi, I coudn't get a hd7xxx as it required pci x 3.0, and my lowly board only supports 2.0
Still very happy to have this working the way I want to, so thanks for your help