Sorry, I thought I had made it clear but I think I may have confused you by prefixing Component with (RGB). I did that because on some web sites selling Component cables and adapters similar to the one I think you have, that is how they're described. It can lead to just the sort of misunderstanding we appear to have here.
The RGB output you can select from the PS2's set up menus is not RGBHV ie. VGA. Unless your monitor will accept the PS2's particular RGB sync on green* output it won't display correctly and probably not at all. I can't tell you for sure whether your monitor will allow this but I'll hazard a guess that it won't. If you've got the cables why haven't you actually tried it out yet?
Remember all you're doing is using some cables to connect two pieces of equipment together. The same PS2 output signal that went in one end is still all that is coming out the other no matter what it is plugged into. Without a transcoder you can't change that.
* I've done some checking for you and the best list for sync on green compatible monitors I've found is on a PS2 Linux website. I think the supported monitor database is quite old though.
http://playstation2-linux.com