But why would you want to modify it to work on a split rail?
Also note that, yes it's true that most ICs will work outside their specifications, but not all will work or be reliable: it's uncharted territory. Another thing is it might work from a 9V bench supply, which has a very low impedance, but a 9V battery is another matter. It might work from a 9V battery for a short length of time, have a distorted output or not at all.