Yes. For a typical American dishwasher installation, anyway, where the dishwasher is connected to the hot water line which is in turn connected to your storage tank water heater.

First, your water heater is already full of hot water that you’ve already paid the energy cost to heat up. It’s therefore nonsensical to deliberately pump cold water from the line into your dishwasher only for the dishwasher to have to heat it up (using energy/money) and then have your water heater also heat up the displaced water inside it that was just pumped out.

On dumb dishwashers that don’t do anything to sense the internal water temperature, this will also moderately improve your wash performance. (GE calls this feature “Automatic HotStart,” for instance. Other brands call it something different. These machines will pause and run their little internal water heater coil at full blast until their current charge of water is at a temperature their programming considers acceptable to start the cycle.)

Modern dishwashers use a surprisingly small amount of water per cycle. Usually somewhere around 3.5 gallons for the entire thing from start to finish. This is contrary to what your parents think, who will insist to you they can totally hand wash an entire sink of dishes with “less water” than that wasteful dishwasher, which they absolutely cannot. Your dishwasher is not consuming water the entire time it is running. It will fill and recirculate that fill’s worth of water inside itself, usually going through 3 or 4 phases of filling and draining throughout the cycle to arrive that that final water usage figure of around three and a half gallons. Therefore it does not readily have access to hot water unless you’ve primed it by running your sink, as what used to be hot water in your pipes rapidly cools off when said water is not flowing. Your dishwasher probably will not draw in enough water in one fill cycle to purge all of the standing cold water that’s in the pipe unless the distance from your water heater to the dishwasher is unrealistically short.

(The latter actually is the case for the dishwasher at my office, which is fed by an undersink “low boy” water heater that’s directly next to it and only separated from the dishwasher by a grand total of about 18 inches of pipe.)