Hi DanielWinnard!
Yes, you can use an option page (https://www.advancedcustomfields.com/add-ons/options-page/). Then in your pages you can do something like this:
<?php
// current page download links (your different set of download links)
$download_links_to_show = get_field(‘download_links’);
// if you dont have links on that page
if(empty($download_links_to_show)) {
// use common download links
$download_links_to_show = get_field(‘common_download_links’, ‘option’);
}