If you want to go with Fusion 360, you can set Fusion 360 off-line and it will operate up to two weeks before it has to go on-line to contact it's activation servers (even though it's free for enthusiasts). At that time it will automagically abscond with your designs and upload them to Adobe, however you can get around this fiasco by deleting some of the Fusion directory structure on your computer before switching it to go on-line.
I asked about this exact issue on another forum & got a different answer. But that particular fellow may have misunderstood and/or 360 newbie. Are you saying if a person was willing to legitimately pay for hobbyist level (or whatever they call the lower priced / non-commercial seat) - you still cant work independently off-line as though you installed all executables on your PC? It still requires internet connection & dependencies? What I was hoping was the typical download/install, design your stuff and only if you are interested in cloud storage or collaboration did you have to be on-line. I could even see a quick connection 'hi, I have legit licence####' and then it lets you work, just to slow down hacker theft. But if a somewhat permanent net connection is required just to do CAD work, I would imagine that could get bogged down & ugly in a hurry on complex parts & assemblies. One day I'm going to have to unplug off the Solidworks $ drug & was just starting to look at 360, but if that's what its about, then Bummer.