Yes, that "volume" argument is quite weak. Note though, that Heisenberg's realm is the quantum level and Godel's is the "non interesting statemets about mathematics", so there is a subjective sense of smallness. I do not have the Good Book with me right now, but as far as I remember Dawkins rejects a personal deity on grounds of probability.
"small." Interesting thought, however, while incrementally small it cannot be denied that quantum increments are computationally VERY LARGE, spanning the entirety of your "knowable" reality of mass, energy and indeed even a vacuum flux.
Do you believe just because Dawkins says it? ("Credo quidquid dixit ________ ...") [Google it, if you have no Catholic background]
Sounds like you just changed the names in the blank.
And is a probabilistic (i.e. - linear) analysis appropriate to a stochastic or chaotic system? When a "trivial" variation from the average can produce a disproportionate alteration in the computational result, linear probability is not a terribly useful tool. The number of possible linear solutions to a truly chaotic probability distribution is uncommonly large. You might catch some tufts of hair, but the beast slips your snare --- and this is of a piece with the quantum problem which has cast its own finely woven net over every aspect of the macrocosmos -- the problem is one problem -- not two different problems.
And because of non-locality, we cannot rule out that what we see as discrete "small" units of quantum process are but "splintered" irruptions into our scheme of perception of an "elsewhere" connected whole. Certainly Bell's Inequality suggested this, and that was David Bohm's extended solution building from that, in which he also posited the nature of human perception.
Some part of the being, the existence, of the quantum process seems also present "there," but not directly perceptible "here." Part of the balloon is stuck through a very narrow hole in a wall. In fact, the whole net of the universe has balloons shoved through its all of its openings. Pushing and prodding a ballon to try and measure the whole thing makes portions of it recede from view beyond the threshold of that barrier, by the very act of trying to capture it. The fact that we seem unable to effectively "drag" the remander of whole through the hole to our side (despite deploying energies not seen "here" since the Big Bang in places like CERN), suggests that portion on the other side is at least equal to, if not far larger than, the part on our side. I am on sound scientific ground at the very least to assert that there is a "there" there.
Either that, or it's turtles all the way down ...