Yes Enchiladas are Authentic Mexican food.
However the authentic Mexican Enchiladas are not cooked in the oven but instead authentic Enchiladas are fried and then dipped in spicy enchilada sauce and then are rolled up with a small amount of meat, vegetables, and/or cheese.
So the enchiladas that are not fried are not considered to be authentic Mexican food but the Enchilada is a Mexican food regardless on how they are made.
Mexicans do eat Enchiladas and it's traditional Mexican food.
I prefer the fried variety of Enchilada over the oven baked Enchiladas but they both are good regardless of how the Enchiladas are cooked.