Thought Experiment: can you reproduce a native app in Java?

Here's an interesting challenge for the Java desktop programmer: can you reproduce an existing native application to the extant that a user would not know? And I mean everything from installation, invocation through usage and de-installation. What would this take? How much native code would you need to write?

If this is possible (and I have my doubts), can you do it again on another platform with a similar application?

If this is possible, can you merge the two codebases? If so, how much sharing can you achieve?