Their original home in their folklore was Atzlan, which of course spawned interest because Atzlan *must be* Atlantis. ;^) Their folklore probably has roots perhaps a two or three centuries prior to the conquest, so, a hard no to that idea.
My recollection is of seeing Aztlan described as somewhere to the west or northwest of Tenochtitlan. I just now remembered seeing small dried seafood like shrimp being sold in the native market(s) in southern Mexico and/or Central America. I traveled to San Cristobal de las Casas (south of Oaxaca) around late 1950s. Then in 1969 traveled by car or minibus through Mexico as far as Nicaragua on the main highway. So at this point in life my memory is a little disjointed. It also occurs to me that the major civilizations in Yucatan and parts of Central America were located closer to the ocean than was Tenochtitlan, and thus had easier access to ocean food resources.