According to the webpage, you only need a WiFi connection once to activate the authenticator application, and after that you're all set.
This comes right after the transition of the EU World of Warcraft account management to the new Battle.net account management. The US transition is reportedly done, although there has been no official world from Blizzard yet (however all their webpages have already changed over).
The app is not available for download yet via Blizzard or from the Apple store. But we'll let you know the second it goes up!
You can read the full FAQ after the break, or check out the Blizzard Support article.