I used to have the wheel that was released as at the time when GT3 was first released, the GT Force. Basically the same color, but no controller buttons where present on the wheel, and it had the GT3 logo in the centre peice of the steering wheel.
This wheel definately worked on the PC when the "Wingman" drivers from the logitech site where installed. The Wingman was the wheel that looked like the GT Force wheel, but was red (and black) instead of blue. With the PC drivers installed, it definately worked in MAME as well (in non-powered mode, no mame games support force feedback to my knowlegde).
Not sure if the same is true for the newer PS2 wheel you have, but I guess you can only try.