I am a satellite technician, I'm not sure what outputs you have on the PS3, but think I can help you.
A hdmi cable to the tv will bring a high definition picture and digital sound to that hdmi input on the tv.
A hdmi cable to the sound system will bring a high def picture and digital sound to that video input on the sound system.
You could also run an hdmi cable to the tv, and a red/white RCA cable or a digital audio cable to the stereo. This would bring picture and sound to your tv, and sound to your stereo. By doing it this way the input you use on the tv would remain constant and you could elect to or not to have the sound system on as well as the volume on the tv on or off.
Another option would be to just run 1 hdmi cable to the sound system. Doing this would mean that you need to use the sound system to uses the PS3.
By hooking it up the way your suggesting you would be switching back and fourth between 2 different inputs on the tv, the one from the sound system or the one without the sound system.
Does that make sense?