Obviously we can only advise on the use of Eventide products. Questions about other products should go to their manufacturers.
That said, the pedal's current requirements reduce at higher voltages, but if the voltage gets beyond a certain point, even for a fraction of a second, it may cause damage. So, a stable well regulated 12V at 400mA may be effectively the same as 9V at 500mA. Note that a poorly regulated 9V may exceed 12V, which is OK, while a poorly regulated 12V may exceed 16V, which would probably cause damage. You can see why we don't want people to experiment with these things.