You’ve gotten a bunch of feedback in your thread on shmups, but the short of it is that, correct, your PS2 component cable will not work; and, since you intend to use the console with an OSSC, you can just get one of RGC’s sync-on-luma cables (or one with a light gun breakout, if you intend to use light guns in future). The OSSC can take composite video and luma as sync without issue, so the CSync cables with the inline sync separator circuits would be an added cost with zero benefit over the others.
As for specifically why your PS2 component cable won’t work, it’s because RGB from the PS1, as it is from most consoles, is RGBS, meaning Red, Green, Blue, and Sync (generally composite video) are each on their own wires(1), and YPbPr component cables only have three, because the sync signal is muxed into luma (Y), negating the need for a fourth wire. If you plugged your component cable into the PS1, the red, green, and blue wires would be transmitting the red, green, and blue color data respectively, but there’s no fourth wire for sync, so the OSSC (or any display) wouldn’t even recognize that there was any video data being transmitted.
If you had a third-party component cable that had an additional wire for composite video (like the first-party Xbox 360 component cables), then you could get RGBS from a PS1 with it, but then you’d also need a custom female RCA to SCART adapter, or a female RCA to DE-15 adapter plus an Extron RGB interface plus BNC to RCA (or BNC plus BNC to RCA adapters) to use it with the OSSC. Much easier to just get a SCART cable.
(1) Generally, when referring to different styles of RGB, each capital letter indicates a separate wire, and a lowercase ‘s’ indicates that sync is muxed onto the preceding wire; so, in addition to the RGBS example above, RGBHV has five wires, three for video, two for sync, and RGsB has three wires, three for video, with sync muxed into Green. (RGsB is also electrically the same as YPbPr, with sync on the same wire, so it’s difficult for devices to discern between them.)