Deploy templates to all users in organization

Yes it is possible.

Actually word was designed with this option in mind.

You are using sharepoint. I don't know if 365/2019 has been updated to handle templates there. But I do know that you can place "shared" corporate templates in a shared (read only for users) folder on your corporate network and make a configuration setting in Word to grant users easy access to that location:

@ File Location- Word 2016 Templates: "Featured" vs "Shared" vs "Custom" location names! -
https://answers.microsoft.com/en-us/msoffice/wiki/msoffice_word-msoffice_custom/word-2016-templates-featured-vs-shared-vs-custom/d23e9c8f-5420-4bcd-84fd-e502e21ab0a5?tm=1477730378693 
Word 2016 changed (again!<sigh> ) the way templates are handled. Unfortunately the names used are not obvious. I've been puzzled about it for a while now and finally tripped over some answers. This wiki summarizes what I've found.

@ Shared Workgroup Templates - Brandwares Best Practices                     John Korchok    January 10, 2019
http://www.brandwares.com/bestpractices/2019/01/shared-workgroup-templates/
Groups of workers usually use the same templates. But it can be time-consuming to keep everyone updated when templates are installed separately on each desktop. Instead, you can implement shared workgroup templates with a feature already built into Office.

Finding Where Templates Are Stored http://wordribbon.tips.net/T006072_Finding_Where_Templates_Are_Stored.html http://word.tips.net/T000862_Finding_Where_Templates_Are_Stored.html
The first step in modifying templates is to find out where they are stored on your system. Here’s the easiest way to figure out that information from within Word.

Hi Chris,

May I know if you try the suggestions shared by Rohn?

You may also refer to Doug's suggestions in this thread Set custom template as default for all users in Word.

Best regards,

Tina

Hi Tina, 

It helped a little bit, but overall I am still in the same place with the problem.

There were too many links and I could not see a way in which I can deploy these templates to other users. The templates are currently stored on my PC and on the organisation SharePoint.

Hi Chris,

Seems you have many templates and want to set up them as the Word templates for all users in your organization.

As you mentioned, navigating to the SharePoint location where the templates are stored could be a workaround.

If you want to set the templates in Word application and let users see the templates when they create new documents, I'm afraid it will need VBA to meet your requirement. (You may check the thread I shared in the previous reply.)

If you want VBA solution, to make sure you get the dedicated assistance, I recommend you post a new question in the category Office/Word/Microsoft Office Programming/Office 2016, members there have more experience about VBA solutions and will help you further.

Many thanks for your patience and understanding.

Best regards,

Tina