Well, technically it is possible, you can look into ReportService, which generates documents based on report and template code.
I would suggest doing that by the means of Cuba security subsystem though. You can restrict editing reports for anyone but the users with Administrators role. I assume you have default role, other then “Administrators”.
You can restrict editing reports via Administration -> Roles -> user roles -> Screens -> scroll down to Other Screens -> report$Report.edit screen -> check deny on the right and click OK.
This will make users not able to edit any reports from the UI.
Concerning Administrators role - you have to trust them to some extent, because there are other ways how they can mess up with the system via Administrators menu.
There are other ways to prevent removing templates exist. You could bind running report to a button and remove the whole Reports menu from the system, for instance. Please comment if suggested solutions don’t work for you.