Would this have worked just as well if a sincerely religious individual who believed in an eventual resurrection of all had cast the patronus?

It would require that they cognitively mapped the existence of the Dementor onto the concept of soul-death and that they forcefully rejected this event on an emotional level instead of just having a quiet factual opinion that it never happened. Such a hypothetical individual is simply a non-reductionist isomorph of Harry's reductionist belief. It would just be difficult for a religious individual to get into that state of mind in the first place. It probably would help a lot if they believed that the Dementor's Kiss actually does destroy a soul.

I mention this because I did think about what would happen if someone like a Buddhist acknowledged the existence of true Death, soul-death, and still accepted that without the tiniest bit of sour grapes; and concluded that although that wouldn't make a Dementor-destroying Patronus, they would be able to see the Dementor's true form and cast a perfect shield against its fear.

Incidentally, Harry didn't say at any point that any of what he said was a certainty.