There’s a rather schocking lack of detail provided here, but in any case you’re much better off not carrying the audio signal on the PCI bus. Your hard drives have to use this bus as well, and there’s no point having your hard drives or your audio run slow whenever you do a file search while watching TV.
The TV card doesn’t really “use” the graphics card. Rather, it sends a block of memory to overlay part of your video memory 60 (or 50 for PAL systems) times a second. This is accomplished by rapid copying of one chunk of memory to another. Your sound could not operate along similar lines because sound sampled only 60 times a second would sound awful. You need a sampling rate of at least 60 thousand times a second before you start getting decent quality. It’s much easier to send this as an analog signal through the cables than to try to convert it to digital, send it through the bus, then back to analog.
The TV card might have a place for an internal cable (consisting of red, white and black wires and similar to the cables your CD drive uses) that can be connected to a free input on the sound card. This, at least, will eliminate the need for an exterior cable.