Can user login the spluk search head?
Authentication configuration is stored in local disk in each search head. So, user can login the search head, but most of configurations in share storage is not available, user can not use any App.
Can scheduled search work properly?
No. Because all configuration in shared storage is not available.
Which configuration will work at that time? The configuration under system direcotry of each search head just work?
User can not use configuration on search head polling. He will need to disable search head pooling if he want to use local configurations.