Dave,

No, All registers have a defined power-on state. And those states are clearly listed in the datasheet. There's nothing random about it.
I've never seen a chip power-up with in-correct states before, so i would like to see what comwarrior found.

People should NOT try to initialize every register at the beginning of the program.
This creates many more problems then it will ever solve, since most people will not bother to read the datasheet to find out what they should set them to.

comwarrior,
What revision is the datasheet you are using?