Cable length is irrelevant to timing. Electrons in a wire are not like mail messages on the road. Individual electrons do not carry a message from your receiver to your speakers.
Information is passed along a wire by inducing a current (moving electrons) along the entire length of the wire simultaneously. Think of it like this: If you had two garden hoses in a big loop filled with water. On one side of the loop your have a pump. On the other side of the loop you have a wheel that is spun by water moving through the hose. When you turn on the pump, the spinning wheel will move instantly. It doesn't have to wait for water to be "processed" by the pump.
The actual speed of the current depends on the resistance of the wire. In a typical house current travels only a couple meters a second -- so if electrical signals were like mail on the road, it would take several seconds for your light to turn on when you flipped the switch -- which of course doesn't happen (barring lights that have to warm up first of course)