Will transaction be rolled back?

Hello,
Today I was investigating some old code that is run in a jee-application.
This is run in a container managed jee-server (weblogic).
I stumbled over this code (a bit simplified):

    public class AException extends Exception {
    }
   
    @Stateless
    @TransactionAttribute(REQUIRED)
    @TransactionTimeoutSeconds(1000)
    public class JobEJB implements Job{

        public void update() throws AException {
         
            boolean ok = true;
                try {
                    //do some update in a databse
                    for(int i = 0; i < 100; i++)
                   
                    if(i==50) {
                        XXXX
                    }
}
                }
                catch (AException  e) {
                    ok= false;
                    sessionContext.setRollBackOnly();
                    throw new AException();
                }
                catch (RuntimeException e) {
                    ok= false;
                    throw new AException();
                }
                finally {
                        System.out.println("Job: " + ok);
                }
        }
    }

I would say that if XXX above is replaced with:

    throw new AException();
   
...then the transaction will be rolled back since setRollBackOnly() is called.
   
    BUT if XXX below is replaced with:
   
    throw new RuntimeException();
   
...then the transaction will be NOT be rolled back, since the exception is catched and I guess the app server will not know about it, right?.

Am I right?

Best regards
Fredrik