What effect would that have, on people as far up as Baton Rouge?
I am betting on "none": Red Stick is what, 70-80 miles NNW of the expected hit spot? Any river push back would be localized to the area within, oh (guessing) 10-15 miles of the center. This is a bit of uncharted terriotory, but the river heads NW from NO and that's a good direction for the capital.
I'm not certain, but believe that there are various spillway outlets along the river to address some of that kind of flooding (or at least the downstream flow of floodwaters.) North of Baton Rouge they Army Corp of Engineers has had diversions facilities for years to channel excess into the Atchafalaya River (roughly a 20 mile wide swamp that would now probably be the Mississippi River if not for intervention.) IIRC there is similar between Baton Rouge and NO, but could be wrong about that.