Okay I did some tests.
The client caught me off guard a bit, but it makes sense. If it's blocked from the network it can still log in just fine with the saved logins(Why re-authenticate offline when it can't mess with user data, right?) and it even has my Library and Collections lists cached so I can use those at least and obviously only the browser part seems to be not working.
Tries to reconnect every time anything is requested.
Basically the auto-installer is self explanatory. It just won't fetch updates, acts like there are no updates and the client works fine.
Tries to reconnect when updates are checked.
The Butler only seems to give an error when a product page is opened and it tries to fetch data for the "installation bar" at the bottom, but doesn't seem to hinder anything else.
Tries to reconnect each time a product page is open.
So the client seems to work well enough in "offline mode" even if the network goes out completely and if it's just a "first attempt blocked" case it tries again each time anything is needed so there won't be any real problems it seems.
The only problems left for me are the icons that I have to change at an update and the fact that each version of each .exe will have a separate firewall rule that I'll need to remove manually(GW still doesn't have a "scan for unused rules" feature), but I'll manage those.
So thanks for all the info and hope I wasn't a burden. At least now this behavior is properly documented for anyone who has the same questions. :)
Keep up the great work!