I've been using Evernote for a long oversesa trip for the last few months. I can confrim that I kept Evernote on my laptop offline for up to 4 weeks - with no issues- the app synced itself when I connected again and opened the app.
The truly annoying thing is the iOS app - regardless -that I had notes (images) saved as favourites or even open before I lost connection - I douldn't view the documents offline mode. This used to be how I kept copies of things like boarding passes, online QR codes for country entry, hotel bookings and such like. I now have to do it all in iOs photos - super annoying. I use Evernote for all my travel stuff including planning and bookings - so this is pure duplication because of a backwards step for the app - it definitely used to work.