The PS2 should output 480i and 480p in component, there's no difference to the signal output than from the GameCube.
On another note, the PS2 itself is incapable of outputting RGBHV video natively. As you'll recall from any documentation on getting RGB setups that's five seperate signals, three colors, vertical and then horizontal sync. You can generate RGB out of the component cables just by switching the PS2 into RGB mode from YPbPr. But it's still not RGBHV, it's RGsB or 'Sync On Green', the H and V signals are merged into the green signal. It will not work on VGA monitors that do not support RGsB/Sync On Green. More over, many monitors that do support RGsB like the Dell P1110 Trinitrons I'm typing this message on, they will ONLY read a 480p RGsB signal or higher. Most PC VGA monitors can't read a signal below 31khz, 480i is 15khz and so a 480i RGsB signal is out of range.
But here's a question, do you have the PS2 in RGB or YPbPr mode with the VGA converter? Cause if it can only convert YPbPr to RGBHV and the PS2 is giving it RGsB, then it could just be unable to correctly convert the signal. Had that issue using a PS2 on a YPbPr TV. The PS2 had evidently been in RGB mode and thusly gave the TV a signal it couldn't figure out. One setting later we got nice YPbPr on a 36" TV.