This is correct, but probably not for the deep symbolic reason you're ascribing to it.
Primals are generally based on "summons" from past Final Fantasy games, and one of those is... Knights of the Round!
So most likely it's just a case of pairing up that summon with the most appropriate setting, and Ishgard is an obvious choice. So the "king and twelve knights" would have been planned as a story element to set up the finale where we fight the primal Knights of the Round.
This really sounds more like Sharlayan than Ishgard!
Where are we told that the Ishgardians are witholding knowledge from the people? Other than the truth of the war, of course, but there's nothing uniquely Catholic about that - the story could have played out the same with a non-religious king or government keeping the same secrets.
I want to point out an important distinction here, because there are two elements to Ishgardian faith - there's the actual worship of Halone, and there's the lies that have been built up regarding King Thordan, the dragons and the origins of Ishgard.
Archbishop Thordan may genuinely believe in Halone, even though he knows and deliberately upholds the lies that have been built up around that core faith.
Now the lies of the Dragonsong War have been shattered, but Halone Herself hasn't really been implicated much in it. I don't see any reason to believe that the Ishgardians are actually abandoning their faith in Her, even if they're restructuring the way the church functions.
Perhaps if you're not religious yourself, maybe it's easy to look at the story and see "religion is bad, overthrowing it led to Ishgard being a better place" but I don't think it's so simple. Much of Ishgard's religion takes inspiration from the medieval church, but there are hints that it's more complex than just "endless holy war" and corrupt clergy - there's a priest working in the Brume, and he implies there's a more charitable side to the religion as well. Aymeric expresses a more moderate faith in a goddess who "would value the lives of Her followers over the deaths of Her enemies". Lucia is specifically a once-atheist Garlean who has willingly taken up the Halonic faith, and says she will pray for us.
As a (non-Catholic) Christian, it makes me glad to see these representations, and not just the "evil religion" that too often comes up in stories, and JRPGs in particular.
There's a middle ground between "harsh medieval religion" and modern secularism, and - even more so in this story-world where magic happens and gods are more likely to exist - there's no good reason for the Ishgardians to actually lose faith in Halone. They just might not be taught such a militaristic view of what She wants from her followers.
(Edit to add: The current effect on Ishgard is probably closer to the Reformation - essentially a split in the church where one side rejected certain Catholic beliefs because there was no Biblical support for them. Ishgard is a rather more forced version, being required to shift because of real-world revelations rather than a theological dispute, but the path could be seen as similar: a shift from 'Catholic' tradition to 'Protestant' reformation of the religion, but still remaining entirely loyal to their god throughout it.)
All that said, the actual state of religion in FFXIV, and what the writers intend to do with it, is rather hard to guess. As far as the vast majority of the characters are concerned, the Twelve are real, and we know for certain that some gods do exist and influence the world (ie. Hydaelyn and Zodiark). But there have been multiple hints that the Twelve might not really exist, or might as well be primals. It's getting to the point that I'm tired of the writers hinting at it, and really hope they give a definite answer about their nature soon.
Perhaps that symbolism is correct, but I've never been aware of it, and I would bet that most other people wouldn't immediately connect "dragons in a fantasy story" with a deep symbolism of pre-Christian Europe.
If I put dragons in my fantasy story, it would be because I happen to like magical flying reptiles and I think they are beautiful creatures. Or someone else might want to put in a fire-breathing monster for their hero to fight. So it's entirely possible that the writers of this story had a similar intention - particularly since they had already introduced dragons (eg. Bahamut and Midgardsormr) as an important element of the story, not connected at all to Ishgard.
It doesn't automatically become allegorical just because you can associate dragons with those things.