The constitution sets no requirements of being a natural born citizen on the Vice President. Basically if Arnold was VP and the President died Arnold would be skipped over and the President pro temp would become the president. Unless of course the Pres Pro Temp wasn't a natural born citizen either then it would go down the list until someone met the qualifications.
That probably is correct about skipping over in the line of succession. Henry Kissenger was foreign-born, I believe, but he was in the line of succession--so he'd have been skipped, I suppose. It's interesting that post 9/11 we really do think of the line of succession going far deeper than just the VP. The reality of the White House or Capitol being destroyed that day brought the horror to life.
