It's not quite as your note implies.

1/
Every PS2, whether NTSC or PAL can play PAL or NTSC games. If your PS2 is NTSC, then a PAL game is classed as an 'import' and cam only be played if it is a backup copy (made with CloneCD or CDRWin) and booted via a modchip installed in your PS2.

2/
Assuming then that you have your PS2 modded, you would take your PAL backup game and play it. Your NTSC screen would display something, but it would either be in greyscale or it would be jumping around dur to the difference between NTSC and PAL.

3/
Each game needs a different patch (it's location specific) to convert the game from PAL to NTSC. There are, in fact, more patches available the other way round. However, if you go to http://www.sgt-dan.com or http://www.megagames.com you will find a list of games and all known patches. If there is a PAL to NTSC patch, it'll be listed there.

4/
If there is no patch listed, then you could buy a PAL to NTSC convertor which sits between the PS2 and the NTSC TV.

Does that info help you?