That would save electricity...but would probably waste more water. IIRC, a German study into handwashing of dishes found that <1% of people actually managed to use less water than a dishwasher. I'd bet it's a similar usage profile for clothes.
Hand washing dishes consumes massive amounts of water because people tend to leave the tap running while they wash. Laundry is typically done in a basin with a fixed amount of water for wash and rinse. I wouldn't place any bets that it uses less water than a high efficiency front loader, but I would venture that you can come close. Remember, we're not talking law of averages here. We're talking about a single person dedicated to the task of reducing water consumption.