put the invisible sprite in a container with the drag/drop object.
The invisible sprite will do everything the object does (and vice versa), including picking.
Yes, this means you have an invisible sprite for every single drag/drop object, but that shouldn't cause your FPS to drop significantly, if at all.
EDIT: I'd still do it the way I said above, but another way, which is closer to what you asked for, would be like:
on touch
pick nearest drag/drop object to touch.x, touch.y
check the distance between the touch and the drag/drop is not too much
and then initiate the dragging that way.