I think that that's similar to or exactly what happened with my dad's paternal grandparents (I've yet to find or see the Non-Catholic license, though). They never got their Catholic marriage licensed signed, and Great-Granddad was by no means an actual Catholic: he and his parents were Anusim due to the pogroms and Anti Semitism in the U.S..
Great-Grandma (z"l) was, however, and she and her parents were B'nei Anusim and Anusim. Her mother's parents (Samuel and Rosalia Korschová Munka) converted to avoid Austrian-Hungarian Anti Semitism, and her dad's ancestors (e.g., the Schwarzenbergs turned Czarnogurskys) converted to avoid both Polish-Lithuanian-and-encroaching-Russian and Hungarian Anti Semitism. By the way, both of Dad's paternal grandparents had Sephardic heritage; and, for example, Great-Grandma's matriarch Helena Dudayová was born a Legrádyova.
Also another sidenote: as I think about Great-Grandma, I feel verklempt. If one had met her even once or twice (and I saw her almost every time, if not every time, that I was up in Luzerne County for Dad's mom's family reunion), she'd've been one of the relatives that he or she would have respected the most. She was literally, as I recall, one of the only ones at the time whom treated me—since I have Cerebral Palsy, and her grandson Jamie, whom also has Cerebral Palsy and developmental disabilities—with as much love and respect as she treated her other great-grandchildren and grandchildren.
From what I hear of my great-granddad, on the other hand and as my granduncle Tony shockingly told me when I said something about my dad and granddad, "Like father, like son." I will never forget that Granduncle Tony wrote that, meanwhile, especially since he normally didn't cross Jack Czarnecki openly (and if you knew my grandfather. you might've been tempted to not stand up to him). Other people talked about how awful Great-Granddad was as well; and I've seen pictures of my dad when he was younger and around Great-Granddad, and you could tell that he did not like him if you'd seen the pictures.
One even had the caption "Doesn't seem to upset at his Grandfather Czarnecki". Dad covered up that part of the caption when he scanned it in and sent it to me.