The short answer is yes, while the long answer is a qualified yes. In a household of 3-4 people you can attribute about $1000 from your yearly electricity bill to hot water.
In comparison, the running costs from natural gas are about a third of the price while solar is even cheaper.
You can save money by using hot water during off peak tariff times, however.
A heat pump is a cost-effective electric option, though, using warm air to create hot water, much like a reverse refrigerator. It works best in warmer climates and is slightly noisier to run.