I'm not sure if this is a valid question. JDBC 2.0 is implemented by a database' JDBC driver. It's not a feature of a database itself. Your Java program either use or does not use JDBC 2.0 features but this is decided when you write your program, not at runtime.
I have noticed on this forum that a lot of people use JDBC-ODBC bridge. You should try to avoid that if a native JDBC driver exists. The bridge is the least efficient.