Pause Game during Game Center Authenticate?

How can I pause the game During the Game Center Authentication Process.

Sometimes the process (depending on internet connection I suppose) takes so long by the time I start the game it interrupts game play and the game continues to play behind the pop up, forcing the player to watch as the character helplessly dies.

Have you tried setting Time.timeScale equal to 0?
That is generally the easiest way to pause a game since everything moving should be based on Time.deltaTime.
Once it has finished loading, set Time.timeScale back to 1.