If you have a centered Sprite at location (0,0) it will sit centered in the scene's origin. If in script, in my case using tool mode, if you use either of the following:
var s = get_node("my_sprite")
or using the
edit_set_pivot() from the node methods, you will see that the pivot/offset is at the origin now, however the sprite image will have moved down 32 pixels.
It's not that it's moving down exactly, it's just that when you use the V key to set pivots, it will adjust a new relative position of the sprite so it preserves where your Sprite visually appeared.