Can we run asp.net application without WEB.CONFIG file?

YES: Because all the configuration settings will be available under MACHINE.CONFIG file, by default these settings will be applied to all asp.net applications. The MACHINE.CONFIG file will be automatically loaded when .net framework is installed. It is something like if we had not defined the web.config the application will take the settings from the machine.config. The machine.config settings are override by the web.config if u defines the web.config for each running application.