Can an ASP.NET web app run without web.config

yes we can run asp.net application without web.config file,if u r not configure any settings in web.config file then it will take machine.config file for default configurtaons.This config file will automatically installed when your application getting executed.

Because all the configuration settings will be available under MACHINE.CONFIG file by default these settings will be applied to all asp.net applications.

You'd have to read the documentation to see the defaults, which for authentication is probably windows, and session mode would be in process.