Upload File Processing Background
After having a look in the Contrib Module space, I would say no, it's not possible. The main problem as you probably already know: A file upload will break if you navigate away from the page.

However, if you have lots of time to invest in implementing this, I could imagine the following workaround: You could ajaxify your whole Drupal website, e.g. with ajaxify so that some outer elements of your page will persist while your navigation is taking place and your content is rendered inside a "content" element. You could then process the file upload in e.g. an iframe that resides outside of your "content" area.

Hope this helps!