We have built this for one of our customers. We had to build a custom word plugin that could be started with an eternal protocol request from Chrome, this can start a local exe on your client, same way Mendix starts the version selector exe when you click edit app from Sprintr. The word plugin communicates with mendix through web services for getting and saving the document. We also use it to create new documents based on templates.
Getting it to work with Word online could also be nice but our customer needed support for the desktop version of Word.
I think the best solution would be to drop Word and create and edit your documents from Mendix directly, probably with an external (web based) solution.
If the client does not mind to edit the document in the browser I would go for the office365 route. This way you do not have a filedocument in Mendix only a link to open that file in office365. But it would mean an integration with office365 to be able to retrieve the links to those documents. In the app store are some modules to connect to office365. And I believe there are some people in the forum that already done sharepoint integrations. They might respond to this question.
Does anyone has more information (or a link to) about this kind of integration? I am looking for the same kind of integration an looking for a starting point with information about the best approach.