Yep.
A typical New Olreanian fast food order goes something like this: "A cheez-burga... wit two meats. Mynaize on one bread. Onion loops. 'n a red coke."
I have lived around here all my life, other than a few years in law school and grad school, and never heard the phase "red coke". I have heard "soft drink", "red drink", or "red drank", but not red coke. Calling all flavored sodas "Coke" is a southern thing, not a New Orleans thing.
And I grew up in The Parish and went to school in the 9th Ward so I'm a bit of an expert on strong Yat accents.