The Church’s presumption is in favour of the validity of ALL Christian marriages, not just those contracted within the Church.
Now, I have no idea if any Gingrich’s marriages were indeed Christian, but he’s probably going to have do some work to straighten out his current situation in any event.
Gingrich may have reason for hope. The brilliant and combustible Willmore Kendall was a professor and friend of Bill Buckley at Yale, and later a writer and editor at National Review. Kendall, the son of a Baptist minister, eventually became a convert to Catholicism and is said to have had three annulments in process at the Vatican at the same time — a record.