Java checked exception not in the function's throw specification?

Normally, the Java compiler confirms that all checked exceptions that are thrown are in the throw specification. Does anything special happen when a native function throws a java checked exception that was not in the functions throw specification list, or does is the throw specification list simply ignored at runtime?

C++

void function(JNIEnv * env, jclass jc) {
    jclass newExcCls = env->FindClass("java/lang/NullPointerException");
    env->ThrowNew(newExcCls, "ERROR");
}

Java

public class Tester {
    static {
        System.loadLibrary( "MyLibrary" );
    }        
    private static native void function();
    public static void main(String [ ] args) {
        try {
            function();
        } catch( Exception e ) { //is it caught? Or what happens?
            e.printStackTrace();
        }        
    }
}

(The C++ function name would probably be mangled. Also loadLibrary should be in a try catch. Don't care, I don't believe it's relevant to the problem. There's possibly other errors in the code, but they're probably not relevant either.)