Would this give him any ground to protest us getting married?

It depends on the state they lived in while together. Each state has their own rules about common law marriage and if they have such a status it is merely based upon living together as husband and wife. So, look at the state statutes where they lived. If in Texas, ask a lawyer about her status.

She should sit down with a lawyer to discuss this. An hour of a lawyers time is a small price to pay to be sure.

Common law marriage requires an agreement to be married, holding out to others as married and thereafter cohabiting in the State of Texas as married. No facts given indicate a common law marriage. Living together alone which is commonly misconstrued as creating "common law" is not sufficient to create the relationship. In any event the more recent marriage is presumed to be a valid marriage as to any prior claims. The other party cannot attack your marriage, but only endeavor to file a divorce if he believes he had a common law marriage with your spouse.