The problems with the Cosmic Race idea being promulgated as official are thus:
1) Indigenous nationalism has accessible national myths and culture to draw upon, and Indian-leaning mestizos will probably go for that esp. if it integrates left-wing worker's agitation.
2) The separation and self-regard of the white immigrant classes/criollo upper class. Race-ideas tend to be right-wing, which would prove a problem when having to combine the landowning class with their indio serfs.
I think the place where this has actually happened is Brasil. Brasil, thanks to its history (a shitload of slaves, the whole Nheengatu thing, etc) adopted Gilberto Freyre's Lusotropicalism to varying degrees, what one writer called "white Negritude". African and indigenous elements were adopted as miscegenation became a symbol of national pride.
Paraguay could also work, given Francia's forced miscegenation, and probably in Gran Colombia as well. Mexico and Peru, I think, would tend towards more indigenist identities given their inheritance of the great megalithic states of the Americas -- but Mexico might be diverse enough both within and outside of the indigenous communities that it could work there as well.
Argentina is too white, and so are Uruguay and Chile, IMO.
America, absolutely not. Miscegenation was banned, too many whites, too many whites who hate blacks, and nowhere near as many indigenous peoples.