Probably not. If you were a test would show it by now.
Depends on how you define "Native American". Teneyuca is an Aztec surname.
The Cherokees did not come to "America." Spaniards discovered "Turtle Island" (The original name of this land) and named it after Amerigo Vespucci.
Other natives came to this land between 650,000 to 20,000 years ago.
NOTE: several false claims have been made that the Cherokee are descended from a lost tribe of Israel (circa 500 BC) this information is based on unconfirmed or disputed DNA testing. A DNA report confirmed in 2009 that the supposed Anomalous Mitochondrial DNA that links the Cherokee to the Israelite is divergent; approximately 30,000 years ago - negating such claims. See link: