When the Desired State Configuration Local Configuration Manager is set in Pull mode it requires a current configuration before it can pull a configuration from a pull server (SMB share was tested in my case). An event with EventID 4131 with a message saying "Current configuration does not exist. Start a DSC configuration first to create a current configuration.".
Even though the error is logged and handled it seems to me that it is a bug that a pull configuration should require a a prior push configuration.