@Amperage,
there are two major questions here that I might identify. one has to do with individual identity and the other with faith, regardless of where that faith is directed.
the individual identity is created in part by its history and experience and in part by its mental makeup which may have a basis in genetic or physical causes and in part by the physical body and its ability to perceive. there is probably more to it, but that will serve as a foundation to build on.
if all the experiences are forgotten, they are removed from the mind-but the effects on the body remain and to an extent the effects on the mind that served to create a particular personality will also remain. the memories may be lost but the experiences themselves are not lost.
I am sure there are documented cases of amnesia and you can read about whether or not cruel people became altruistic or extroverts became introverts etc, or whether mathematical aptitude had been lost or gained, love relationships disappeared.
it seems to me that the results would vary depending on how strongly the characteristics of personality had been adopted. preferences for tea or coffee, chile peppers or spinach might change...
but I think the issue of faith is something else. people can reach an intellectual conclusion about religion, they can choose one religion over another, but the question of where does faith come from is not quite clear. there are people who have lived through miraculous events and yet see nothing beyond the physical. there are people who have suffered tremendous heartbreaks and yet they have faith in some benevolence in the cosmos.
so the question of whether or not a person has chosen to believe in God (or anything else or nothing at all) is not so much based on experience, knowledge or even personality, in my opinion. spiritual traditions may call it grace, which is not something to get into on this thread, but would make a great thread maybe in the theology group. so if that had descended on a person, I think it would remain. and if it had not, I think there is always a chance it will come, regardless of whether or not a person is changed by amnesia, alzheimer's, or any other life situation.