If the USA was formed as a "Catholic" nation, it would not have turned out anything like it did. Arguably, there never would have been an American Revolution at all.
In the late 1700's, the Church was still very much a temporal power, and frankly, had essentially a stultifying effect on individual liberty. Only Holland and Britain, Protestant nations, developed representative governments and embraced individual rights. Catholic nations like Spain, Portugal and France remained pretty oppressive.
Not looking to flame, I was born and raised a Catholic and don't have any axe to grind with the Church. But the historical record is pretty clear.
While I understand what you're saying, I think the determining factor was inheriting the concepts of representative democracy from the British, rather than the particular brand of Christianity. After all, France, a heavily Catholic nation, followed our lead within a decade or so with the French Revolution and many of the Spanish colonies in the Western Hemisphere also eventually followed suit.
So, while I think I agree with you that many of the concepts on which this country was founded were derived from Protestantism in Europe, Catholic people were adopting them as well, and it wouldn't have precluded the American Revolution.
We'll never know, of course. BTW, I'm not Catholic and never have been, so I raised the question purely out of curiousity.