If you're referring to the float switch, its only function is to interrupt the power to the fill valve, if the water level rises to a predetermined level--which would cause it to leak or be splashed out the door. It is possible for a leak to migrate into other components, like the drain pump, if it is severe enough.

While you're servicing the float assembly, check the switch for proper operation: It is normally closed, when the float is down; and should open as the float is lifted away from it.

This switch does not control drain function. Check under the sink, where the drain hose goes to your drain (and garbage disposer, if you have one). If n the drain hose is clear and unkinked, make sure it loops as high as possible before going to the drain. It is also possible that the drain pump itself may be partially obstructed.

Run water into the dishwasher, and then select "Cancel/Drain". Listen to see if the pump motor continues to run throughout the drain cycle. If not, you may need to replace the pump.