I think once they hit the Gulf of Mexico hurricanes can veer anywhere from west to northwest to northeast depending upon other frontal systems coming from the west or north. They rarely seem to keep a straight line for too many days, so NOLA probably has less to worry about then everyplace else on the Gulf coast...... (but what do I know?).
As one who has a vested interest in these matters, and one who has watched hurricanes for many, many years, you are very astute in your assessment. ;o)