I don't think any American Monarchist (I am one) considers monarchy a possibility for America presently. I think that an aristocratic system with a monarch balancing and limiting the excesses of the nobility is a natural development of any free society; I think that a healthy society does have a dominant religion and merely tolerates other religions. I also think that Protestantism is the dominant American religion at least for the time being.
Does "not a possibility for America presently" mean that Catholics should be trying improve the possibility for it in America, at least in the future?
Not just Catholics, everyone. It is good for America, so it would be good for as many people as possible see that as a historical goal. The least we all can do is to stop using "monarchy" like a swear word often not realizing what it even means.
It is true though that since monarchy is often a happy historical experience for Catholics, and far less so for Protestants or other confessions, you are likely to find more monarchists among the Catholics. Among the Orthodox, especially, they are quite a sizable minority of the faithful.