Yes indeed, even for the shortest routes.
The processor needs about the same time to calculate a rhumbline or a great circle.
The permanent bearing of the rhumbline is just in theory; it is updated as often as a GC course, to correct for wind, wave and current drift, compass errors or steering precision.
However, here the question from a non-navigator was about disproving the ‘flat earth theory’ with great circle sailing. I hope that he understood my basic explanation.
What I do not know:
Does ECDIS calculate a GC on a mean spherical earth, or a Geodesic on an ellipsoid earth?