Elements that are assigned to the grid will not have any flow applied, there is no way around it. They will be slapped onto the grid one over the other, just as if they were absolutely positioned. They will obey any z-index value, though.
This is because the specification explicitly states that the elements are allowed to overlap, if they are assigned to areas that intersect.
Also, the specification encourages to mix grid with flexboxes, to obtain more complex layouts.