Check the Logitech website for the G25, it lists the games that the G25 is compatible with. They do show the G25 as compatible with the PS2, but I have not tried it.
Yes, the G25 works fine with the PS2. Games see it as a Driving Force Pro. None of the games use the clutch and shifter as far as I know, so I splurged on a PS3 shortly afterward.