Yes, a dirt bike can start and run without a kill switch. The kill switch is a safety feature designed to quickly shut off the engine in case of an emergency or to stop the engine from running. It is typically a button or switch located on the handlebars.
If the kill switch is faulty or missing, you can still start and run the dirt bike by using the ignition switch or kick-starting the engine, depending on the bike's specific starting mechanism.
It's recommended to have a working kill switch installed and functional for safety purposes. If the kill switch is not working, it should be repaired or replaced as soon as possible.