It's very likely possible. Like Megalomaniak said, the export is a precompiled program along with packed game data. If two games use the same exact export template, then I don't see why you couldn't do that with them. After all, the Godot editor actually runs on Godot code. However, it seems unlikely that there would be an API to do this as there isn't much demand for it and making that API would be a challenging task. You would probably have to create a customized export template with some new biolerplate C++ and some SCONS modifications to include the Editor resources you would need to run the "inner" game. That's just my guess.
I've seen Unity embedded in a native Android app before, so anything is possible.