Yes. In the same way that dishwashers are an order of magnitude more water-efficient than washing by hand. (But consume a kilowatt of electricity heating the water and running the pump, which is the part that everyone always leaves out.)
When my water heating was electric, switching to a dishwasher consistently led to lower electric bills compared to a year prior (confirmed for 12 whole months).
You save water and electricity.
You heat the water when you wash dishes by hand too, don't you? It's not very hygenic to do dishes with just cold water.
Given that by hand you use much more hot water than the dishwasher would, you're using more electricity (or gas). Since a little pump doesn't use much at all, it's mainly just the drying heat that matters. Though nobody is forced to use the drying cycle - if one enjoys drying dishes by hand, they can still use the dishwasher to do the washing.