The HD convertor box would have nothing to do with the PS or the GC. It just brings the signal in from either a satellite distributor or the terestrial antenna.
I\'d think you would just plug it right in with the component cables, but to get progressive scan you would need the PS2 adapter which as far as I know has not come out yet. Although there are some 3rd party ones that I wouldn\'t trust. But I\'m an idiot so it may already be out and I just don\'t know about it.