Andi,
I think you misread the question. StudentATP was asking what happens if you fly the initial track heading and don't change it.
Unless you are flying a track along the equator, you would eventually end up at the North or South Pole, if you had enough fuel. This is easy to see if you plot a rhumb line on a Mercator map of the world, where a rhumb line is of course a straight line. You will never get to your destination.