Do simple LED strip dimmers consume power while turned off?
Yes they will. It may be a few milliamps, or even less, in the microamp range, but they will as the microcontroller and passives are still powered even when the microcontroller is asleep or simply has it's PWM timers off. Since it is an RF accessible controller, it will need power for it's radio receiver interface.

The only way to get to 0 power is a physical switch. And the power supply would still be connected, so a physical switch on the power supply's AC side as well.

As to exactly how much power, get a multimeter and test it. It won't be much.