The NDK is not native per-se. It is to a large extent a JNI wrapper around the Android SDK. Using NativeActivity gives you a convenient way of dealing with certain app-life cycle events, and add your own native code on top. ALooper, AInputQueue etc. are all JNI wrappers of the Java SDK counterparts, some with additional code that is private and unaccessible for real apps.
When it comes to Android development, there's no such thing as writing an application entirely in native C++ - you will (in every real App case that I can think of) always need to use the Android API:s, which are to a huge extent pure Java. Wether you use these through wrappers provided by the NDK or wrappers that you create yourself doesn't really change this.
So, to answer your question: No, it wouldn't be worthwhile, because you would end up writing JNI wrappers for SDK calls instead of writing JNI wrappers to your own Java methods that do the same thing, with less code, simpler code and faster code. For example, showing a dialog using "pure c++", involves quite many JNI calls. Just calling a Java method through JNI that does the same thing will give you faster code (one JNI call), and, arguably, code that is easier to maintain.
To fully understand what you can do, you really must examine the Android source code. Start with native_app_glue.c, which is available in the NDK, then continue with the OS implementation of AActivity, ALooper, AInputQueue etc. Google Code Search is a great help in this. :-)
If it is easy to do in Java, and includes many calls, call a method through JNI that does it all, rather than writing all the extra code to do it with multiple JNI calls. Preserve as much of your existing C++ code as is reasonable.