I don't know how GameAnalytics builds, but the idea is that because a module's code is blended into Godot, it's like having Godot as a project, to which you want to add a GameAnalytics dependency.
So it's mostly about telling SCons to include that. It depends on wether you want to add GameAnalytics as a dynamic library, static library, or directly copy/paste of the code (which is the simplest).
Sorry if it doesn't helps that much, but that's the main idea. I'd be curious myself to see how it's done with libraries having their own build system. You could have a look at existing modules to see how it's done, eventually :)