Any type of configuration operations via SNMP will require read-write access. The safest way to import a config from one device to another is to copy the new config to the startup-config, then reload the device. This can be done using CLI or SNMP (via the CISCO-CONFIG-COPY-MIB). For example, from the CLI:
copy tftp://x.x.x.x/export.cfg start
reload
If you were using CiscoWorks Resource Manager Essentials to do this, I would suggest using Config Editor, and pushing the configuration in merge mode.
You can certainly do this to the running-config, but certain commands may not apply correctly until the device is reloaded.
However, if both routers are currently online, then this would be a mistake. You would have to change enough of the config (e.g. hostname, IP addresses, etc.) to make it unique.