Different color themed 3D View for different Mode?

I’m learning animation/rigging and keeping on forget which mode that I’m currently in or not turning off/on Auto key. Is it possible to have 3D View’s background color change based on modes? Like a mode indicator of sort.

Probably no, it isn’t possible, at least by standard means. Maybe you can do something like that with Python scripting, but unfortunately I’m not that proficient with Python. Try to look and/or ask in the Python Support section.