J2ObjC is best suited for "fat-client" apps that have a lot of non-UI code; after all, it was developed by Google's Inbox by Gmail team. Like the other apps who had the most success with j2objc, sharing code across platforms was an initial requirement, so designing and developing code that is platform-independent was always important. The chances of success are much lower when porting an existing an Android app, as the platform-specific code is frequently interleaved with anything that can be shared. A quick test is to search for Java files that don't have "import android" statements -- approximately 70% of Inbox's Java code is shared, so 2 of those 3 files in your sample app should not have "import android" in them.
Even if your app mixes Android calls all over its source, there are still good reasons to refactor your app to extract portable code. First, shared code provides consistent behavior across platforms. New features can be released on all platforms at the same time, and documenting them is easier (docs can be shared, too). And because your team didn't need to rewrite the logic behind those new features (just their UI), these features can go public more quickly than if you had separate Android and iOS teams.
Quality is better, too. For example, if you find a bug in the Google Sheets calculation engine (good luck, as it's very well tested :-), that bug is very likely to be present across all platforms. That sounds like a weird benefit, but it means the bug will be noticed, reported, and fixed more quickly. Shared code is easily tested with JUnit, since the difficult test areas like database and UI interaction are separated out. Those JUnit tests should also be translated, built and run on iOS, to verify behavior doesn't change across platforms. One nice synergy is that portable code is easier to test, so investing in unit tests encourages separation and isolation of shared code.
Finally, once an app is refactored to be more portable between two platforms, it's much easier to add a third. Many Google apps that use j2objc also use the GWT compiler to port the platform-independent code to run in browsers. Because the UI wasn't included, they are then free to pick whatever web compilers and frameworks they want to finish the app, such as Polymer and Closure.
So I personally discourage developers of existing Android apps from using j2objc, unless they plan on converting their platform-specific app into one that is largely portable. It hard to realize the benefits of tools like j2objc unless your development team is fully committed to cross-platform design, development and execution. There is no quick hack to get an Android app running as a quality iOS app (or vice versa), and we can't pretend there is to our community.