I installed CartoDB on a local machine and it worked fine. However, when I tried to go offline I was able to login, but I wasn't able to do anything. It looks like the page is looking for online data. Is it possible to completely work with CartoDB in an offline mode?
Short answer, no. It requires many many assets from the web.
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Actually I've just tried the CartoDB native Android version, and it does indeed work offline. I've been able to see previously downloaded maps, from the Package Manager activity.
Now I'm investigating on how to use it to build my own mobile app. Based on the CartoDB library.