try with resource, will resource clean if thrown exception is not caught?

CoffeeCups :

What happens when a try-with-resource throws an exception which is caught outside? Will a cleanup still be performed?

Sample:

public void myClass() throws customException {
  try (Connection conn = myUtil.obtainConnection()) {
     doSomeStuff(conn);
     if (someCheck)
       throw new customException(somePara);

     doSomeMoreStuff(conn);
     conn.commit();

  } catch (SQLException e) {
     log.error(e);
  }
}

The part I'm concerned with is when the customException is thrown. I do not catch this exception with the catch of my try-with-resource. Hence I wonder if the connection cleanup will be performed in this scenario.

Or do I need to catch and rethrow the connection, like this:

public void myClass() throws customException {
  try (Connection conn = myUtil.obtainConnection()) {
     doSomeStuff(conn);
     if (someCheck)
       throw new customException(somePara);

     doSomeMoreStuff(conn);
     conn.commit();

  } catch (SQLException e) {
     log.error(e);
  } catch (customException e) {
     throw new customException(e);
  }
}

Olivier Grégoire :

Yes, the cleanup will happen... if the close() method correctly handles the cleanup:

Example of execution

public class Main {
  public static void main(String[] args) throws Exception {
    try (AutoCloseable c = () -> System.out.println("close() called")) {
      throw new Exception("Usual failure");
    }
  }
}

(shortened by Holger in the comments)

Output on stdout:

close() called

Output on stderr:

Exception in thread "main" java.lang.Exception: Usual failure
    at Main.main(Main.java:4)

Example of execution with an exception thrown in the close() method

(suggested by Holger in the comments)

public class Main {
  public static void main(String[] args) throws Exception {
    try (AutoCloseable c = () -> { throw new Exception("Failure in the close method"); }) {
      throw new Exception("Usual failure");
    }
  }
}

No output on stdout.

Output on stderr:

Exception in thread "main" java.lang.Exception: Usual failure
    at Main.main(Main.java:4)
    Suppressed: java.lang.Exception: Failure in the close method
        at Main.lambda$main$0(Main.java:3)
        at Main.main(Main.java:3)