Not really
Sorry, Falleron, but I´ve got a PS2 too 😉 and there is no option to connect the console to the Apple LCD. The LCD has an ADC Connector, this is digital inclusive the power for the screen. The PS2 only has RGB-Scart in the best case. And even then it would output DVDs tinted in green without a software hack... You cant get the PS2 picture on the screen...
Except for my solution: Use Formac Studio (rules if youre into video) and connect the PS2 via Chinch to the Studio and use Tevion to display the PS2 on your comp screen! You can even watch TV with it, BUT it requires a lot of processor power to display it smoothly in full resolution.
Advantage: PS2 on your Computer! You can even capture scenes and gameplay with Tevion or iMovie or compatible in full speed and resolution!
Disadvantage: Display is slow with my iMac400 (maybe 12 fps?), and captured image is only transferred via Chinch (-->less image quality.. but you won´t recognize that when watching it on TV - or even convert it to QT)
Hope ths helps!🙄