No, it is not possible to change the position of the banner in the ArcGIS Online for Organizations home page. The banner must stay at the top of the home page.
Users cannot modify the position of the banner on the site; however, the user can customize the logo, image, style, border, or text features within the banner area by using HTML code or a rich text editor. A comprehensive reference of what is allowed can be found in the Related Information linked below.
Note: For best results, the recommended image size is 960 pixels wide by 180 pixels high.