My experience is with the Aztecs of Tenochtitlan, so I will not provide an all encompassing answer. That being said, the answer to your question is yes. The noble families and rulers of Tenochtitlan almost certainly believed in their religion, as much, if not more than the common population. The idea of people not believing in the popular religion of their culture is a recent idea. It is impossible to isolate religious belief from Aztec culture and warfare, because they are so tightly intertwined.

Aztec noble families usually sent their children at a young age to schools to become either priests or warriors. Both of these positions are incredibly important for the Aztec religion. It was the duty of the warrior to go to battle and capture prisoners for sacrifice, and it was the duty of the priest to practice all the rituals and ceremonies required to pay tribute to the gods. These ceremonies were also incredibly ritualized and scrutinized. Priest students were beaten relentlessly and worked to exhaustion. Priests would pierce their ears and tongues with spines to harvest blood for ceremonies, drawing reeds as thick as a finger through holes in their tongues. Families would not put their family members through such ordeals simply to maintain an illusion of pomp and ritual. Geertz argues > "Power serves pomp, not pomp to power" meaning that leaders did not use religious institutions to achieve more power as we are so accustomed to assuming, but in fact power was used achieve a closer relationship with the divine. In this context, spiritual contact was a goal in and of itself, and not necessarily tied to any political objective.

It should be pointed out that 'Native American' is a term that encompasses a insanely huge variety of people, it's like saying 'Did Eurasian rulers really believe x?', it's an almost monumentally vague task.

Did you have a specific group in mind? Inca, Maya, Mexica, Pueblo, Iroquois, they'll all have different answers.