If an aircraft flies straight ahead, does it follow an orthodrome/great circle? I understand that an orthodrome (line on a great circle) is the line with the shortest distance between two points on a sphere.

If an aircraft flies straight ahead, i.e. there is no wind, the rudder is not actuated and the aircraft is parallel w.r.t. the surface of the earth underneath it, will it follow an orthodrome/great circle?

I also understand that a loxodrome is the line that one follows when keeping a constant heading. This is the point where I'm confused, because wouldn't that mean that when flying straight ahead/along an orthodrome, the heading/bearing would constantly change? In other words, does this mean that one needs to turn in order to keep a constant heading?

EDIT: My question is not "which line does one follow when keeping a constant heading" (a loxodrome, I know that) but rather "what line does one follow when flying straight ahead (in the hypothetical case of no wind and no control inputs)?"
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..