Just for the record, this device converts the signal only. Also, it is a PAL to NTSC converter, meaning you put in a European game in, and it converts the output to an NTSC signal; what you want is an NTSC to PAL converter.

If your PS2 is not chipped/swap disc'd, the game will not play at all, since it's a PAL console and an NTSC game. The converter deals with incompatibilities between the PS2 and the TV.