I have never heard of this software. The hardware is so different that I just can't believe in such a thing. It might be possible, if you run a specialized linux kernel on a hacked PS2 which has wine installed and some very simple old games, but the work involved to get everything working is simply not worth the hassle.

BTW - the PS2 did have a hard drive, it came with FFXI preinstalled. Some PS2 games even let you install parts of them onto it in order to speed up gameplay.