Hi Jusc,
so, offline mode allow you to use your online maps only from cache. So you can see map tiles that you already saw or tiles that you downloaded with "SQL shared mode"!! Did you used this mode? If you use "SQL separate mode", you download map as separate file and you have then select this map is second tab "Custom maps".
So when you have enabled offline mode, there is no need for internet connection. I already tested this and seems that this work. Please play with it a little and I believe that it should work. Simple test is to watch some places in online mode, then switch to offline and restart application (to reload maps). You should see only your cached maps and on places where is no tile, you'll see only white area without any text.
Did this work for you? If not, I'll send you my testing version. I did some improvements on map loading, so maybe this is "fixed" now (if there is any problem) ...