Yes, every region in the US has a definite accent and dialect but even within regions there are language variations among ethnic groups.
For example, in my region of the South Carolina Lowcountry, there is, of course, a regional accent. Within this same region though, the accent and dialect further differentiate between urban white Charlestonians and rural black Gullah/Geechee natives. Both groups live within a few miles of each other geographically but culturally they are worlds apart.
Another example would be NYC. They are all New Yorkers but they aren't all the same ethnic group. Each ethnic group within NYC has its own accent and dialect.
People's ethnic cultures do influence their language separate from just their geographical regions.