You can try it, but I suspect HDMI will likely overrule the others. Besides that, the effective range of component video is pretty short (like 10ft before you start getting signal loss) and HDMI is only like 30ft before you need some kind of signal booster or repeater. So, I'd wager that even if you COULD get it to work like you wanted, you'd still need some kind of signal booster to get it to the other room.
Does anyone know if the ps3 will output component and hdmi signals simultaneously? I have a plasma in one room and a projector in the next room. I would like to connect them both at the same time without a switcher or splitter.