Not a silly question and I hope that, when the experts answer this post, the two points I am about to make aren't deemed to be silly too.
The first is that, unlike your globe (I suspect), the earth is not a perfect sphere. It is an oblate spheroid, fatter at the Equator than at the poles. Thus any real great circle track will appear not to be a straight line on a spherical globe.
The second point concerns Coriolis acceleration. Any object moving at a constant velocity in a rotating reference frame (and the Earth turning once a day is a rotating reference frame) will experience an acceleration, both the magnitude and the precise direction of that acceleration being given by the vector product (2 times the earth rotation vector times the aircraft velocity).
It's difficult to explain vector products on a flat sheet of paper, but suffice it to say that the Coriolis acceleration experienced by an aircraft travelling straight and level at 500 mph directly over the North Pole (in any direction) is 0.107 ft/sec-squared, towards the tip of the port wing. (Tracking Eastwards along the Equator, the Coriolis acceleration is vertically downwards. Tracking North or South over the Equator it is zero.) Thus any aircraft straight and level in the northern latitudes will experience an acceleration (and hence drift?) to port. But I am not sure if that would affect tracks - rather, I would expect it to affect the heading you would fly in still air in order to achieve a certain track, and that heading would vary with latitude.
For what it's worth! As always on PPRuNe, I await the expert answers with extreme interest!