A slow water current would result. This current would NOT be shaped like a narrow beam that moves from appliance to bathtub drain. Instead, the water would spread in all directions from the appliance, the entire liquid contents of the bathtub would slowly move away from the appliance and towards the drain, and the flow would slowly contract inwards and ooze past the drain plug. There would be no spot in the bathtub where the water stayed still. If the appliance fell very close to the drain, then yes, the fastest current would exist between them.
Electric current takes a similar path.
Charges in all parts of the tub are sucked towards the drain, and at the same time they are pushed away from the appliance. All the charges in the water are driven into motion, and an electric current appears everywhere. A human body contains salt water and is a good conductor. Human skin is resistive unless it has been soaked in water for a time, so human skin is usually conductive too. A human body in the tub is therefor transparent to the flow of electric charges.