While the component output of the PS2 can be set to RGB, almost all PS2 games run SD (480i), while PC monitors can only go as low as 480p (VGA). Very, very few PC monitors (all of them older ones) support the lower horizontal scanning rate (15kHz) required for 480i. You would need an upconverter to deinterlace the 480i to VGA in order to display it on a PC monitor.
If the game you're concerned with just happens to support the progressive scan feature of the PS2, it is a slight bit more possible, but getting usable sync out of the PS2 when running progressive scan and the component output is in RGB mode is extremely difficult. There are also products designed to "trick" games which normally do not support progressive scan into running in that mode anyway (at the possible expense of some video exactness), but the concern with utilizing the component output in RGB wrt getting a sync signal still applies.
I guess to succinctly answer the question: no, not really.