Is it possible when uploading a file to a node for it to upload as a background process? Ideally what I would like to do is to be able to upload files in the background while being able to continue navigating through the website. When the uploaded files are complete a notification appears on the website to say that the upload is complete or an email is sent.
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!