No. Alligators (Alligator mississippiensis, A. sinensis) are freshwater reptiles. They inhabit:
They lack salt glands to excrete excess salt, so they cannot survive in full-strength seawater (35 ppt) for extended periods. The American crocodile (Crocodylus acutus), found in South Florida and the Caribbean, does tolerate saltwater and lives in coastal mangroves and estuaries.
Marine zones (intertidal, neritic, oceanic, abyssal, hadal) are defined by depth, light, and pressure for marine organisms. Alligators are not marine; they do not occupy any ocean zone.
If you see a "gator" at the beach, it's almost certainly a crocodile—or a lost alligator that won't last long.