Does an HDMI graphics card always pickup the audio

My p6540y (bought 2010) uses DVI to the monitor and a dedicatedaudio connection to the monitor's speakers.  Works fine.

I know the HDMI standard supports the audio signal (works fine on TV), but the integrated graphics does NOT have an HDMI port.

If I install a current model HDMI gaphics card in the PCI-E x 16 slot, can I be certain the audio signal will be passed through the HDMI cable to the speakers in the monitor?

If not, what other steps that must be taken?

Dave