Even without using the big data extension, it should be possible to connect to Hive via JDBC. I've tried with different drivers for Hive (Hortonworks, Simba) but the registered driver never appears as an option when you configure a database connect node.
yes it is certainly possible. Once the driver and all its companion libraries are registered in the database preferences page via the add directory button the driver class should be listed in the dialog of the Database Connector node. For more details see this post. If the driver is still not listed have a look in the KNIME log. It should contain information about the registered drivers and all potential errors. To view the log file open KNIME and go to View->Open KNIME log and search in the log file for the path of the JDBC driver you registered.