Short answer is no. The problem with the WoW authenticator is that it is a mathematical equation. Any mathematical code can be hacked. Just like your accounts password. Blizzard Entertainment has put so much hype in this authenticator security that people just blindly believe it is the cure all to account security issues.
You may have already heard complaints from authenticator owners who have gotten hacked. Top MMORPG news reporting sites have already pointed out that these things do not work. The crazy thing is that Blizzard Entertainment is now talking about making the WoW authenticator mandatory. What will change when everyone has one? Hackers will get smarter and more of them will be hacking authenticator enabled accounts.
The problem isn't in how much information people enter to access their account, the problem is in who else is viewing that information as they enter it. Other companies do not even have close to the problem that Blizzard does with their accounts being hacked. Would it not be more lucrative to hack someones PayPal account then it would be to hack their World of Warcraft account? Yet you just don't see it happen as much with other websites. This is why many World of Warcraft gamers feel Blizzard Entertainment is partially to blame for this rash of attacks.
Another problem crops up when talking about the WoW authenticator. The WoW authenticator is really only designed to work when it is actually attached to account. Do you know how easy it is to get customer service to remove your WoW authenticator from your account? You only need to have a few bits of personal information to remove the authenticator. Most people could get this information if they simply hacked your e-mail account and because they have your e-mail account hacked they can then have your Battle.net password as well.
The majority of World of Warcraft players have no desire to learn about how hackers are hacking computers everyday. They simply want to sit down and enjoy the game each night when they get home from work. When Blizzard tells them that the WoW authenticator does work, it is much easier for them just to believe Blizzard then do the research to actually find out. Take it from me, if you want your items, account, and personal information to stay safe you should try reading a bit more into how hackers hack WoW accounts.