By default, the <html> and <body> elements fill the viewport whatever its size.
IF the footer is a “sticky footer” that follows the bottom of the content below the bottom of the viewport OR sticks to the bottom of the viewport if there is insufficient content to push it below the bottom of the viewport,
OR if the footer is fixed to the bottom of the viewport and never moves even if more content is added above it,
THEN no future elements would appear below the footer.
IF the footer is NOT a “sticky footer” and the content is insufficient to push the footer to or below the bottom of the viewport,
THEN, YES, a background-image applied to the <body> element will appear below the footer.
That’s how the <body> element works unless otherwise restricted by dimensions (not usually recommended).
Hope this helps somewhat.