There was a bug in the game launcher around version 2.0 that meant that you couldn't use the Steam version without an internet connection even if you put Steam offline, but I was under the impression that it was fixed in the EE version, which is what you will have. If there's still an issue then yes, picking up the GOG backup would solve it.
I don't have the Steam version installed at the moment, so I can't check it. Is anyone else able to? As the OP mentioned, the problem was if there wasn't a connection, rather than just setting it to offline.