Yes, all four of the "Civilized Tribes" did (the Seminole, being essentially Creek refugees, operated under a more traditional tribal government, I believe). I wouldn't be too quick to attribute these governments to contact, however: cf. the Iroquois Confederation, whose republican government far antedates Columbus. (Leading some overenthusiastic scholars to attribute the US Constitution to the Iroquois, a stance which most scholars now agree is unfounded--but the idea nevertheless lingers on in popular history.) Much more remarkable is how quickly Native societies took to gunpowder, horses, metallurgy (by the 18th century the Iroquois were noted for their silversmiths and goldsmiths), and European textiles. As Pushmataha noted, by the 18th century Native American life was inextricable from European goods; the sort of nativism Tecumseh espoused would have been impossible to implement.Speaking of Cherokee, IIRC they created a semi-independent constitutional republic with well-established institutions by their own even before the removal. The Hawaiians had accomplished similar achievements - they were still largely a tribal alliance under Kamehameha I, but by the time of Kamehameha III, less than half a century later, they became a constitutional monarchy which went though a massive land reform.
I was always fascinated by these "speedy" modernization process conducted by the indigenous people as they are really, really uncommon, and wonder if accomplishments like these can be represented as an in-game civ ability - for instance, the ability to rush though the civic tree when behind the world era.