Er, no, all of it would be possible. There is absolutely no need to have a permanent connection. And hey, even if we assume that it wouldn't be possible, why not make the cloud stuff an option that you can turn off? Maybe some people are responsible and keep their computers backed up and would rather not lose access to the game they paid for each time their internet connection flickers.
As soon as you store some data locally, you have to do a lot of sanity checking, and synchronisation is a pain, and so on.
Personally I think you should have the option of making an 'always offline' character, with no access to the AH, but I think that would involve Blizzard putting too much data on the client side -- which it obviously doesn't want to do.
I remember back in 2000 using gamespy to see which games my friends were in and join them with a single double-click, pretty much friction free.
I don't see why being able to hex edit is necessarily a problem, if I want to play through the game with a fully decked out character why couldn't I?
Always-on DRM will never be a good idea.