Hmm, sounds interesting. If, say, we tie it in with a *Joseph Smith-as-Frère André, would that essentially mean an early alt-version of the Knights of Columbus as well?
Yeah, if you were gonna do Joseph Smith as a Catholic Saint, I think you'd want him to be a founder of a Catholic lay movement and maybe one that regular Catholics see as kinda dodgy or controversial because its somewhat outside the mainstream. I think a much earlier version of the Knights of Columbus, especially if it had private "rites" that weren't unambiguously just for fun would do the trick.
The way I'd see this playing out would be that Smith might have a fairly idiosyncratic understanding of Catholicism and would mostly be laboring independently in the American frontier and in missionaries to the Northern European poor, as OTL. So his organization is fairly non-standard and has other unique elements to it. But since its in America and is succeeding among people that the Catholic Church can't reach very well in this time period, he gets a lot of slack/doesn't have a lot of oversight.
After his death (his martyrdom?) writings and practices come out that give Catholicism a fair amount of heartburn and require quite a bit of apologetic ink rationalizing and explaining away. But by this time his movement is too tied in to the Catholic Church to be condemned by the Church or for the movement to break away, so a compromise is muddled out.
This could have interesting sociological effects on the development of American Catholicism and therefore on the development of American society as a whole and on the development of Catholicism as a whole.