If this happened, you've see a survival of the fittest case as the variolated group rapidly expanded their territory into areas depopulated by smallpox, which would in turn affects the groups around them and shake things up big time.
I've also thought a way for this to happen is to have Chinese or Japanese colonisation of the New World, and have the natives seize a doctor (skilled in traditional Chinese medicine) in a raid, and have them apply variolation to an outbreak of smallpox, which if things went right (enough people survived who otherwise wouldn't) would allow variolation to spread. The Pacific Northwest, where Asian colonisation is likely to begin, has societies of the complexity that this might work.
As noted, this would take some luck, since variolation would be more risky amongst American Indians than other peoples and something which is probably lethal is unlikely to catch on. But if it becomes a cultural practice, then you'd see what I described above. Unvariolated groups are pushed out or assimilated (or just killed from disease), variolated groups survive (with losses). It would be interesting to see how Europeans can settle North America in these conditions.
That's not even to mention how far this practice might spread. Could more Western Amerindian groups rebuild more effectively? Stronger Puebloans? An effective successor of the Mississippians? Pacific Northwest coalesces into states capable of fighting off Europeans, or at the very least, can become a native-ruled state once freed of colonialism?