Hand-washed dishes: No! Use boiled (then cooled) water, water from an alternate source, or after washing with dish detergent rinse for a minute in a dilute bleach (1 tablespoon of unscented bleach per gallon of water). Allow dishes, cutlery, cups, etc. to completely air dry before use.
Home dishwasher: Yes, if the hot wash is at least 170o F and includes a full dry cycle. However, most home dishwashers do not reach this temperature. If you are uncertain of the temperature of your dishwasher, rinse in dilute bleach and completely air dry as described for hand washed dishes.
Commercial dishwasher: Yes, if it is a NSF listed washer and manufactured and operated with a heat sanitizing rinse set at 170oF that lasts for at least 30 seconds. Additional information on commercial dishwashers can be found in the fact sheets for food service establishments.
CAUTION - "Green" or "Environmentally Friendly" dish washer additives, which may be advertised as a disinfectant or anti-microbial, are weaker disinfectants and should not be relied on alone to eliminate potential pathogens.