After digging into the Nashorn code, I did not find any references to the javax.json packages. However, I did find the following comment in JSObject:
This class can also be subclassed by an arbitrary Java class. Nashorn will treat objects of such classes just like nashorn script objects. Usual nashorn operations like obj[i], obj.foo, obj.func(), delete obj.foo will be glued to appropriate method call of this class.
It would be fairly easy to wrap JsonObject and JsonArray in a JSObject implementation.
Edit #1
As it turns out the ScriptObjectMirror class can be used as a go-by or as a default implementation of JSObject itself.