Yes, you can indeed have a full-width site as you seek.
Indeed as you will have read on the information about this. Weaver Xtreme Plus allows you to specify a background image for specific areas on your site, including a full screen site bg image, background images for the wrapper, header, container, content, sidebars and more. You easily pick any image from your Media Library to use as the background image.
Weaver Xtreme Plus is available here: https://plus.weavertheme.com/
Hope this helps.