It seems to me as if, no, it does not… it seems to me the Control Ob. acts ‘only’ as an Empty… therefore it does not matter what shape the object is … would love to be wrong, though!
Nope, read the description when you mouse over it. It reads “Control object:If available, its location determines the center of the effect”.
The blender manual description for the modifier https://www.blender.org/manual/modeling/modifiers/deform/cast.html
Cheers, guys!