Some do and some don't.
Many of the ones with tuners, also include audio inputs, but not all.
If they don't have them, the capture software can sync the audio from your sound card's inputs.
Check the software for this.
This seems to work better than you might think.
I've got a real time DV capture card that also has analogue inputs. This has its own break out box with all connections, but even on this expensive card the audio is looped to the line-in on my soundcard. As stated above I think this is the normal rather than a cheaper work-around.