Yes. The camera must be in Playback mode (power off, press 'Play' button, lens does not open/extract, last photo taken shown on LCD) to output video to an external display over the USB splitter.missed you here
do you mean that it show the image from the lcd screen in tv if and only if camera review the images.
Apparently the ptpcam interface does support live view capture and image download to a PC connected over USB. That's probably the way to go here instead of having to make custom cables (see ptpcamgui for what can be done over a USB connection to a Canon camera running CHDK).