The aircraft will follow a curved path to the north of the great circle.
I do not believe that the above will always be the case.
At the Equator there will be no ER or TW, so you will flt along the Equator.
When going west in the northern hemisphere at a ground speed equal to the rotational speed of the Earth at that latitude, the TW will be equal and opposite to the ER, so there will be no wander. This means that you will fly along the parallel of latitude on a 270 true heading.
If you fly west at any higher ground speed the TW will be greater than the ER, so your track will be south of the Parallel of latitude.
I could be wrong of course.....this age-induced brain fade is a terribly sneaky creature!