Does NCM have the ability to (after performing a config backup of the device) perform a write mem on a Cisco device?
No, it can't be done via the backup job. You'd need to create a new job that issues a "copy running-config startup-config" to all devices.
Just like superfly99 mentioned, it is only possible with a separate „write memory job“.
if you have separate vendors, you need to build dedicated jobs for each vendor to issue the specific commands.
you would then run the job after your nightly Config backup job.