Is Mississippi and parts of Alabama, Tennessee, and Kentucky one giant island?
Rhetorical questions:


Does the Erie Canal, which connects the Hudson River with Lake Erie make northern New York, southern Quebec, all of New England, all of New Brunswick, and the non-island parts of Nova Scotia an island?
Does the Chicago Sanitary and Ship Canal make all of the eastern part of the US an island?
Does Russia's Unified Deep Water System make Finland, Scandinavia, and Estonia an island, and mainland Europe another island?


Humankind has learned to connect waterways with canals, locks, and dams. The sudden appearance of those canals, locks, and dams does not suddenly make those now disconnected lands into islands. The connection between the Tombigbee and the Tennessee rivers involves manmade canyons, manmade canals, and several manmade locks and dams.

What about naturally narrow waterway connections? As an extreme example, consider the Committee's Punch Bowl in Alberta, Canada. This little lake has two little outlets. One of the outlets eventually joins the MacKenzie River, which flows into the Arctic Ocean. The other eventually joins the Columbia River, which flows into the Pacific Ocean.

This leads to one last rhetorical question: Does the natural existence of the Committee's Punch Bowl make most of Washington state, most of British Columbia, almost all of the Yukon, and all of mainland Alaska into a very large "island"? Most geographers would say no.