Yes, it's possible. But you wouldn't ordinarily want to do it if both devices are going to be on the network at once--you'd get an IP address conflict.
Here's how you can do it with a manual twist that lets you tweak it so you don't have conflicts: Display the startup-config from one device in NCM--let's say it's a Cisco 1941 router. Copy it all and paste it into Notepad, then edit the device name, IP address, gateway, subnet mask, etc. so it's unique. Save the file. If you don't want to change anything, make sure the original device is off the network before you proceed.
Next load the config into the startup of the second device. It can be as simple as using tftp to move the file from your PC or NCM into the startup of the new device.
The details will be slightly different for every different device, but if NCM is already set up properly to download and upload configs, it's easy.
Keep in mind that you might want to load this config into the running-config of the new device for testing. If it causes conflicts, or if you lose the ability to remote into that device, you can have someone at the device reboot it and you'll get the original config up and running from the startup-config--that way you can recover in case of issues. Just remember not to write mem or copy run start until you're certain you want this new config in the startup.