Xbox one runs on Windows 10 and can run apps developed for the same platform. That being said, is it possible to develop an app for Xbox that emulates the PC version of windows 10 and can run executable files and programs? Can use this app to run a version of Blender that begins a render on startup?
XBox One does not run any old Windows app, it runs apps developed for the Universal Windows Platform (UWP). To run on an XBox One, Blender would have to run everything that accesses the operating system through that API.
The biggest stumbling block for that would be OpenGL, as XBox's interface to the graphics hardware is done through DirectX. It doesn't support OpenGL at all.
Based on that, I'd say it's not possible.