Path Controller GameObject parent / attach to another to another Moving GameObject.

[chiako3D]

Hi,
I am not sure I understood the setting your are describing.
A spline controller will follow a spline. This is true independently of the existence/movement of the controller's parent. And it will follow the spline's movement, independently from whether that spline movement is due to modifying the spline's transform or its parent's transform.
Does this answer your question?

OK I understand but is it possible at run-time, I meant after you press play? 

GameObject(parent) -> Translating In Wold space
  |
  GameObject(With Path Controller Component)

That is what my question meant I hope is Clearer 

*the path animation follows with parent*