There's already an API for native activities. While I doubt that Google will be the one to release the framework to write Rust applications, there's no reason why it would be impossible to interface app-level Rust with the Android SDK.
The big problem with such a setup, of course, is that the application itself would be running inside a JVM/Dalvik VM, so the app would constantly be switching between Java and native, which can't be great for performance. However, it can be done; thankfully, Chrome and Firefox aren't completely compiled to byte code, the JIT and rendering code is written in native code. With Mozilla's use of Rust in their browser, that means that there's already a significant Rust runtime running on Android, at least.
If the app uses Rust and a library to hook the draw call, it should be fairly easy to write the app like a video game and render everything in Rust. This would come bundled with a tonne of accessibility problems, of course, as every rendered control would be a non-standard one.