Yes, the water will come back down the Mississippi. However, the river is very deep and wide around the mouth. The river can absorb the flow.
There will also be significant, and varying, delays for the storm runoff to make it's way through the various watersheds it's generated from to drain back into the Mississippi, and then down the Mississippi. The water won't come back as a large "slug", but rather as a broad "mound" dispersed over time.