Perhaps, but...
This would require a Registry edit on each computer and will not put your sharepoint templates as the first button in Backstage, but will show your templates as the default templates for choice.
See Registry Hack for Backstage to Show Custom Templates by Default and try using the value of "2" instead of the "1" shown on my page for Custom templates.
Note, I do not have SharePoint and am guessing here. If it does not work, it can be changed back to 0 or 1.
It is possible that this can be done using Group Policies, but that is beyond the scope of my knowledge.
This is a consumer user-to-user support forum. You might get enterprise-level answers at the sister site: office-word-itpro - Microsoft Q&A