No, not via the regular Mendix’ Studio or Studio Pro. You will also not see the document's text in the browser’s inspector as it does not get sent along to the frontend at all.
Maybe there is a possibility to use the Mendix SDK, but that is a totally different story.
But the idea to make it possible to show the page property document's content at the frontend is very useful. Should even be in the elements that have a translations. Maybe you can add this as an idea. you will have my upvote.