In fairness, the Anti-Revolutionary Party of the Netherlands was decidedly Protestant (if as traditionalist conservative as Christian democratic before pillarisation started breaking down), the Scandinavian Christian democratic parties are more than non-entities, and the CDU does have at least something of a Protestant influence even though it's the de facto successor to Zentrum more than anything, but I'll concede that I'm grasping at straws here/couldn't resist the opportunity to bring up early 20th century Dutch politics.
That aside, I could definitely see the People's Coalition metamorphosing Christian democratic elements at some point, but I don't see that happening any time soon. Alexander the Average has a very good point about the Catholic interests and Patton's interests being diametrically opposed to one another given that Catholics are still the majority religion of recent immigrants during this time period, not to mention that Catholics are presumably the most Progressive group after Jews. Certainly, I could see Catholics becoming less tied to the Progressive unions and machines over time in the same way that Catholics became decreasingly Democratic over time; but I doubt that such a social change will come for at least a generation, particularly after Patton's dog-whistling designed to appeal to the WASP working class. Perhaps LBJ could attempt to incorporate ideas (or more importantly the rhetoric) of political Christianity into the People's Coalition, but I just can't see such ideas making the People's Coalition a true Christian democratic party, so to speak, given its decidedly populist origins as a party of the Southern WASP working-class. The People's Coalition could expand to be a party of the WASP working-class relatively soon, and it could eventually incorporate more European Catholics into its ranks after they become assimilated into American society (especially if a version of the Immigration Act of 1965 is passed, which would thereby help create a new class of immigrants alongside Puerto Ricans and Latinos), and it would probably be desirable to use some rhetoric based on Christian principles. But does that make the People's Coalition a Christian democratic party? I doubt it; instead, I think it's more likely for the People's Coalition to evolve to be a "hardhat" party, so to speak, supporting a synthesis between vaguely Christian principles, nationalism (both economic and cultural), a two-thirds secular, one-third religious social traditionalism, and economic populism/leftism. There are Christian democratic elements and probably a corresponding faction, to be sure, but it's not a fully-fledged Christian democratic party.