Not this Catholic. Not now, not ever.
He’s still married to wife number 1, whether he likes that or not. If he sincerely wished to repent of his sin of adultery, he would return to her, instead of trying to seek blessings for his earlier behaviour.
I admit to being biased on this because I’m pro-Gingrich, but are you aware that his first wife was his high school geometry teacher who he married when he was 19. I’m not on any diocesan tribunal and I’m suspicious of the entire process these days but I’m willing to give the tribunal the benefit of the doubt at least on marriage number one.