God only exists where there is faith. Without faith, there is no God.
Katras don't. Spock wanted to play it safe either way. If you believe in them, then it ironically saved his life.
Since Star Trek is not The Real World and is a work of fiction, then Spock, Vulcans, and Starfleet don't exist either. But since we're talking about the confines of an established fictional universe, you're blowing smoke. According to Star Trek, the katra exists. You don't live in the Star Trek universe, so your own religious beliefs don't count.
Whether or not God exists in the Star Trek universe is a different dicussion.