You can CERTAINLY do this. I do it.
The PS2 actually can be set to run the RGB colorspace on its component outputs, which makes it very easy to do. The classic thing to do is grab a SCART cable, hack the end off, use the CVBS (yellow) line to recover sync using a LM/EL1881 or similar (since the RGB is not sync on green), and then feed all that to your monitor. You'll have to go into the shell menu and set the component outputs to RGB, since they defualt to YPbPr (which won't damage anything, but will result in a very green picture).
Oh, one more thing: this won't work for progressive scan games. The PS2 disables its CVBS output when running 480p (since you can't run composite video with those timings). This means that while it'll happily output RGB video at 480p, there's no sync information available. Design flaw, if you ask me.