If your garbage disposal stops working, you can still typically run the dishwasher without needing to turn off other appliances or fixtures under the sink. The garbage disposal and dishwasher are typically connected to separate electrical circuits and plumbing systems, so a malfunctioning garbage disposal should not directly affect the operation of the dishwasher or other under-sink appliances.
However, it's always a good idea to exercise caution and be aware of the electrical and plumbing connections in your specific setup. While it is unlikely that running the dishwasher would accidentally activate the hot water heater or other appliances, it's important to ensure that they are properly installed and wired.
If you're uncertain about the specific configuration or concerned about potential issues, it may be helpful to consult a professional plumber or electrician. They can assess your setup and provide guidance on any necessary precautions or steps to take to ensure the safe and proper operation of your dishwasher and other under-sink appliances.