libgdx – create a game with a native android code and a game engine?

I want to create some kind of (simple) jump and run the game for Android with a game engine (like for example libgdx). Now, I'm wondering if it is possible to create the less demanding graphic parts in the native android (like the main menu of the list of high scores, etc.)?

And if it is possible, would not it be better to develop everything with the game engine?

Here, as a simple diagram, how do I imagine the flow of the application:

application flow diagram

Some basic information: I have some Android development experience, but I have never used a game engine yet.