Another argument for a separate 12v supply: Whatever it is you are using to supply 9v to your whole shebang is going to be supplying a heckuva lot of current to this one effect. Maybe you have mA to spare, but maybe not. That, plus all the simplification that comes from not having to boost your voltages at high current levels.
Then again, why not power everything off a single hefty 12-18v 2-3A supply, with regulators, buck converters or even voltage dividers (and whatever filtering you need) to drop you down as necessary for all other required voltages? It seems to me that life is easier all around if you start with the highest voltage you need and drop, rather than boosting & dropping willy-nilly all over the place, with all the complexity, space & noise challenges that implies.