I get the sense that you're using "becomes true" (in the title of your post) to refer to the scenario in which more and more people say it and believe it to be true. But that doesn't make something true. The proposition is either true or false. People's beliefs about it are irrelevant to whether it's true. But I could also interpret your post as aiming at a reductio ad absurdum on the use of that principle ("human logic doesn't apply to God"), like Richard Dawkins' flying spaghetti monster (and its devoted Pastafarians).
But it's interesting to consider: Some humans did think they landed on the "logic" of God (e.g. arguably, Plato, Spinoza, Leibniz, Hegel). But notice that the people that think they know the logic of God tend to be people who believed in God (I guess that would go without saying, since you couldn't think you knew the logic of God if you didn't think that God exists). So the problem isn't with the proposition "human logic doesn't apply to God." The problem is that the people who use that premise also violate that premise (i.e. they dismiss human logic on the grounds that no human can know anything about God, while claiming to know something about God). You certainly can invent your own religion and justify any objections to its doctrines with that principle, but then you'd just be being as irrational as the people you're objecting to here.
No one can debate about anything that "human logic" "doesn't apply to." And what can't be debated about, doesn't exist.