If an aircraft flies straight ahead, does it follow an orthodrome/great circle?
There isn't a perfect answer to this, but effectively yes.

Anything that moved in a completely straight line would of course leave the curved  surface of the Earth and go off in to space. And realistically no vehicle of any kind could perform the (lack of) manouvers described above with no control changes.

To perform the best approximation of 'straight flight' while staying on the surface of the Earth would mean deviating from the true straight line only in a direction perpendicular to the Earth's surface. This in turn means staying in the plane defined by containing the vector of direction of initial motion and also the centre of the Earth. The intersection of the Earth's surface with this plane - i.e. the path the craft would actually follow- would be the great circle. And in answer to the last part, yes, when flying a great circle the heading constantly changes. 

EDIT: This does, of course, assume a reference frame relative to the Earth, as pointed out in comments..