This should work fine. That's exactly how most people have been implementing the login process, including all of my apps.
What I meant by "Only use tabs at the root level" was:
When your main view doesn't have a tab bar, but when you tap an item, it does a push transition, and the new view contains tab bars at the bottom. This is not only discouraged by apple, but also a weird interface. You probably wouldn't see any popular apps on the appstore that does something like this since it's not user friendly.
That said, in your case, once you sign in your root view is the view with the tab bars, so that's not what I am talking about in the disclaimer, and totally encouraged.