In theory, it could be possible, but then again do you really want to risk messing up your PS2? You'd have to open the thing up and hook all your gear things to their proprietary connections, then get your hands on the method to format to their file system (again, made by them for them, I'm sure they don't just hand that out). To top it off, how are you going to get the PS2 copy of the game without the HD and NIC adaptor? They come packaged all together. It would be more trouble than it's worth and you might wind up toasting your PS2 in the process.

I think the real question in my head, however, is why you would want to play on the PS2 when you have the option of playing on your PC? I know there's been several old threads buried around here discussing the benefits of PC vs. PS2 (and I'll admit that I'm strongly pro PC) so I won't get into the details about it, but needless to say the perfrmance and amount of system control on the PC is far superior.