In your hypothetical, are presuming that the AZ Secretary of State will discover - without equivocation - that Obama was born someplace outside the US?
Or, are you thinking that the Supreme Court in finally settling the definition of "natural-born" once and for all, will define it in such a way that it will preclude Obama from eligibility irrespective of actual birth place?
For my own $.02 - I think if the AZ SoS does somehow discover Obama was born someplace outside of the US, there's still a remote possibility that the Supremes could craft a definition of natural-born that would include birth on foreign soil. That's unlikely. But, it's also unlikely that the Supremes would create for themselves the authority to actually remove the President. I'm guessing that they,d leave it to Congress to impeach and convict Obama of fraud, and just craft a decision that would allow AZ to keep him off the ballot. That is assuming, of course, that they'd hear the case in the first place, and not pass for justiciability reasons. Whatever would happen, I don't think it a stretch to call their decision the most important decision since Marbury.
Assuming Obama was born in the US, I doubt that this Supreme Court would craft a definition of "natural-born" that strays very far from Ark in it's definition of citizen at birth. I suspect - as an attorney and avid court watcher - that this court would define natural-born solely based on the principle of jus soli. The odds of them finding that a child has to be born to two citizen parents and on US soil very, very slim.
I have read a lot about this stuff, which has been around since 2008 at the latest. But I really haven’t completely mastered it.
What about the age of Obama’s mother? Often that’s discussed in these arguments.