It depends of the game. But I have never eard of a compatibility between a PS2 game and PC game for any game.
UT PS2 for exemple doesn't have an internet multiplayer mode (only iLink), does it ?
UT came out for PS2 during US launch, loooong before the network adapter was available. So no, it has no network support. I too have not heard of any PS2 games which work with PC versions.