The static cache export is a function that precompiles the pages that would otherwise be dynamically generated by PHP.
Images, documents, and other media files are not processed by the server through PHP, they are just delivered like the static HTML pages are, and therefore don't need to be static cached.
You can create your url using ezroot in the template instead to create a direct link to the file in the var folder. Just remember that as other static cache no user permission is checked.