Is there a preference that would cause that layer to be in every new document?
Not really. If I wanted what you want, here's how I'd do it:
Create a large artboard to serve as your repeating brand background; large enough to fill the screen with the pattern at the desired size. Add your repeating logo artwork and whatever else you want, (background color, etc.).
Now add an artboard within the first, (choose the artboard tool, hold down Shift, click/drag). Get the size and location of the inner artboard where you want it, (centered within the outer one, I would think), and save as a template, (.AIT).
Load the template. Paste or create customer artwork on the inner artboard and take your screenshot.
