The FluentUI got some progress loading components but they can only be applied to the add-in (which is a web application) only.
Is there anyway to display a loading overlay over the entire word host application as opposed to displaying on the add-in only?
Web add-ins are still very limited in UI customizations. The best what you could do is to create a popup window using Office dialog API. Read more about that in the Use the Office dialog API in Office Add-ins article.