The rumors about it not working on characters is crap.. however it doesn't seem to kill monsters at all. It seems to affect all GBA versions of this game...

Further testing shows that it does work on monsters, except monsters under the Charm status.
The timer doesn't seem to do anything while under Charm status, and even after Charm status is removed, the timer continues to be stuck.

Ok, I think I understand this better after testing.
Monsters normally throw out "Slowing Petrify" attacks tend to not do anything in its initial stage (1/3 Stone). It
always takes 3 Slowing Petrify attacks total to move to the next stage (2/3 Stone). Subsequent Slowing Petrify attacks don't seem to accelerate/move the timer for 2/3 Stone.. as that timer seems to work independently.