I don’t think so since the Hauppague expects component video (YPbPr) and you’re outputting RGB SoG. You could email Hauppague and see if they think it’ll work, in my experience they reply to emails decently fast.
I typed up a lot here but it was getting contrived. Short version:
I’m not aware of a capture card that can capture RGB SoG (doesn’t mean they’re not out there). IMO your best bet to keep it as simple as possible, so if you ask me you should get a VGA-capable capture card (AverMedia makes a few, no clue as to their quality but they’re cheap), use a VGA splitter (may need a powered one), have one output from it go untouched into your monitor, and the other with a SoG->RGBHV circuit in-line into your VGA capture card. Or if your monitor doesn’t support SoG, put the circuit before the splitter.
FYI this is basically all speculation since I haven’t done this before.
My “component to VGA” SoG cable came from Fry’s, if there’s one near you I think they have a decent return policy, you could just take it back if it won’t work. Be sure to set your PS3 to do RGB out since if it’s expecting RGB SoG instead of Component, you’ll get incorrect colors. You’ll probably need some RCA jack couplers if you get the same cable I did, which has male jacks instead of female.
There are probably premade SoG -> RGBHV converters out there if you don’t want to build your own.