can a theme functions file trigger events outside the theme?

Wondering if its possible for a functions file (which I assume gets "triggered" upon activation) can be code to preform an action that would normally have to be done manually?

Specifically, the theme activates and then imports a DAT file via an Import Customizer settings plugin.

My challenge is that I designed a bunch of themes that require settings from the Customizer to function. I didn't realized New Blog Templates only works when creating a new site which is a problem for many users because they often want to change their themes later on. Fortunately I found a customizer import plugin that copies everything over... I'm just trying to imagine a way that this could be automated somehow.