No sir, you are not correct
Actually head pressure is equal to density x gravity x height. The diameter of the pipe doesn't actually effect head pressure, only the height difference between the two water levels. However pipe friction also adds to head loss and the larger the pipe the less friction. In other words 1" pipe will flow the same as 6" pipe in theory but with pipe friction the 6" pipe will actually allow more flow than the 1" pipe. The bigger the pipe the better!