I did some work in this area; I don't think there would be major problems. The annoyance is that it's not just a single line of Java you need to write -- basically any event you actually want to use (screen touches, rotations, anything like that) requires a thunk to pass it into your NDK. On the plus side, once done, done.
You'll also need to think about whether you'll need to leave C++ and go back to Java to do things (to access other features on the phone). If you want to write something that uses screen taps and draws things, the work is pretty simple. If you want to start talking to servers, do GPS or use the camera or things like that then it gets complicated fast.
You can do this transition into C++ at any layer BTW -- you could do game logic in Java and the rendering in C++. It's just a call into a shared object -- a DLL.
Why did I do it? Simply because I'm more productive in C++ because I'm more familiar with it. If you're starting from scratch, you may be better off choosing the path of lesser resistance and working in Java.