what exactly does a 'no mod' patch do?

Can't be done. The PS2 has to boot first and that is where the "secret" things are done by Sony to read pressed areas of the original game (that normal readers/burners can't reach) in order to check authenticity.

Certain modchips, like Messiah, fool the PS2 into thinking that it has properly read the CD/DVD and provided the correct booting data to allow the game to be loaded.