Assuming you have the following deployed to your users:

• OneDrive for Business sync client
• Microsoft Sign-In Assistant
• Office 2013 / Office 365 ProPlus

(I haven’t explicitly validated this, but it is what I have installed on my test PC)

…then configuring Office to use a SharePoint Online library for Shared document templates is pretty easy.

Using a registry entry, you can simply set the following key to the WebDAV URL of the Document Library.

Windows Registry Editor Version 5.00

[HKEY_CURRENT_USER\Software\Microsoft\Office\15.0\Common\General]

"SharedTemplates"="\\\\[email protected]\\DavWWWRoot\\path\\to\\templates\\"

I will follow up this post at some point with the ADMX route.