Yes, it does. My TV also have a scart input. However, the PS1 resolution via component isn't supported neither.
To answer some of your original questions component does not have a better picture than RGB. Actually, RGB is above component and is the native internal rendered color space of most video sources at their most primary stages. Particularly, the PS2 has artifacts that manifest around edges and a little noise on top with component output.
If you wanna go the RGB route, I'd say get the RGB SCART cable first and see if your TV will take 240p over that route... because I'll be damned if I ever recommend a cheap scaler before all else.