I can't guarantee the Mac will behave exactly the same as the Windows
version, but it probably will. The graphic can be in the drawing layer and
still be in the header -- those are two separate considerations.
Open the header area. Select the graphic. If you see the Picture toolbar,
click the Text Wrapping button and choose Square (or any other except In
Line With Text). If you don't get a toolbar, then right-click the graphic,
select Format Picture, click the Layout tab, and choose Square.
The picture should still be the same size, in the same place. The only
difference may be that text in the header moves around it; this can usually
be fixed with the use of tabs or paragraph indents. Close the header pane.
Now the picture should obey the print option to omit drawing objects.