However, it seems like for 12c, we need to have a database schema for even a simple component (from the FMW 12c infrastructure stack?).
You are correct. In order to get Fusion Middleware Control you need the infrastructure. The infrastructure requires an Oracle Database and schemas.
3.1 Understanding Oracle Fusion Middleware Infrastructure
Oracle Fusion Middleware Infrastructure is an Oracle Fusion Middleware distribution that provides Oracle WebLogic Server, Oracle Coherence, and the Oracle JRF infrastructure services, such as:
Oracle Application Development Framework
Oracle Metadata Services
Oracle Platform Security Services
Oracle Web Services Manager
Oracle Enterprise Manager Fusion Middleware Control
These services are installed into the Oracle common directory inside the Oracle Fusion Middleware 12c Oracle home by the Infrastructure installer.
Note that the equivalent installer in Oracle Fusion Middleware 11g is the Application Developer 11g installer, which requires an existing installation of Oracle WebLogic Server. In 12c, the Oracle Fusion Middleware Infrastructure distribution consists of both Oracle WebLogic Server and the Oracle JRF in a single installer.
So, can I get an EM extension template installed without having to go for a Oracle DB provisioning?