New Orleans would not be able to support deep sea commerce trading and more importantly the entire city of new orleans and surrounding areas would not have a fresh water supply. The intakes to the water plant would still be under water but the water would be either brackish or full blown Gulf of Mexico salt water. The city of New Orleans water plant does not have the means to remove salt from water. This is significant. Baton Rouge gets its water from wells tapping the Baton Rouge Aquifer. However, over time there is a possibility that the aquifer could become brackish. Baton Rouge Water presently has scavenger wells to the south of their well fields to intercept brackish water infiltrating the Baton Rouge aquifer from the south. Baton rouge could not function as a deep water port either.
Morgan City and towns above and inside the basin would be in peril. Interstate 10, highway 190 and possibly highway 90 could be severed.
It would be a significant (almost cataclysmic) event should the Atchafalaya capture the Mississippi. Could it be reversed, probably, but it would take time and several boat loads of money. However, the environmental damage would be significant and would take a long time to reverse if at all. Unfortunately, we being humans, think that what is currently the situation is normal and should stay that way. However, in geologic time frames and perspectives we not even a follicle on the butt of time and we are insignificant. If the Mississippi River decides it's going to change course it damn well is going to do it and there is not much we can do about it. It has done it in the past and it will do it in the future. As Carl Sagen was so fond of saying "the laws of physics (nature) are universal and they cannot be broken".