Well, since the
Fallout timeline diverges sometime in the 1950s, Native Americans had about thirty years of full citizenship rights before then. So in the decades before the war, many could easily have left the reservations and climbed the social and economical ladders to later afford a place in the Vaults. Sadly, it's possible that the people still living in the reservations were impoverished, and it's damn near unlikely that those survived the bombs and radiation.
Any that succeeded in securing a place in a vault would probably end up a minority. And after a few centuries, you'd be unlikely to see if anyone alive currently was of Native descent, and it's even less likely to find anyone even aware of their heritage, history, and beliefs (a lot of American history is largely forgotten among the wasteland populace). And in the
Fallout universe, there doesn't appear to be any sense of racial and cultural identity among (mostly) non-mutant humans, so you're not likely to find any area inhabited primarily by a certain ethnic group, not without some special conditions (like San Francisco in FO2).
EDIT--
Fixed some mistakes regarding the Fallout timeline.