You are correct in your perceptions. The vast majority of pedals have their circuits energized as soon as a power source is hooked up and there's a cable in the input jack (assuming they use the stereo jack ring method to complete the ground connection for current to flow). The footswitch serves to connect the effect circuit with the signal path entering and leaving the pedal, but not to turn the power on and off. The LED is only indicating the position of the footswitch--engaged or bypassed--and not whether or not the effect circuit is energized.
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