I've noticed that several games state that they have Progressive Scan support. Is it possible for my PS2 to support this feature, or is it only new HW models?
You actually have to hold Triangle and X at the same time at the Playstation 2 logo boot up screen to activate progressive scan in some games like SSX3. I don't know if that's for the majority of EA's games though.
Because although progressive scan is a hardware feature, it must be triggered by software to be activated (see Gamecube games), and the DVD drivers in the old PS2s do not support progressive scan. It's simple really.