WCS and NCS use SNMP to fetch the configuration from WLCs. This happens when you manually go to Configure Controllers --> Refresh Config from Controller from the WCS/NCS dashboard. (You can also use Background Tasks to automatically backup controller configs on a schedule, which is done using a combination of SNMP and T/FTP).
If you look at a packet sniff of the traffic between the controller and WCS/NCS during this process you will see several hundred SNMP Gets and Responses. What appears to be happening is that the configuration is being pulled piece by piece from the controller, and not as one gigantic configuration file in a single SNMP query. Based on what I see in the sniffer capture, I think it would be a significant undertaking to try to do this with a 3rd party tool or a custom script.
As an alternative, you may also find automated backups using SSH scripts and TFTP or FTP, which we recently talked about in another discussion:
Transferring Crash file from standby: Login to the Active WLC in HA.
From CLI: (Cisco Controller) >transfer upload datatype crash (Cisco
Controller) >transfer upload filename (Cisco
Controller) >transfer upload mode tftp (Cisco Controller) >transfer
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