Almost certainly not, as it is a logical fallacy. If there is no "God," there is nothing to discover or not discover; there will always be a "gap" allowing some to believe that there is indeed a deity of some sort, and we simply cannot discover such a thing. If there is a "God," we logically cannot use tools and methods that would inherently be a part of such a deity's creation to prove it exists ... the whole game board pieces proving that there was a creator to the game board thing.
I do think God's existence can be proved deductively and certainly don't think it's a "logical fallacy" to believe as such; there have been logical *proofs* - not merely probabilistic arguments - for God's existence by philosophers for millenia. While we can't fully know the divine essence, we can deduce from classical theistic proofs from thinkers such as Aquinas that there must be a ground of all being, change, and contingency that itself can have *no limits* to its knowledge, power, etc. So while we can't fully understand omniscience, for example, we can know what God *is not* - that is, not having limits to knowledge - and as such we can have a real knowledge about God's existence and his attributes without fully understanding them.
