I don't think the God question is "unanswerable" due to the Heisenberg Principle. As far as I have thought about that one, I also have the suspicion that the question is unanswerable, but due to Humean principles. I think Hume here is still applicable in some corrected form. Take this rationale:
Hume's main argument concerning miracles is the following. Miracles by definition are singular events that differ from the established Laws of Nature. The Laws of Nature are codified as a result of past experiences. Therefore a miracle is a violation of all prior experience and thus incapable on this basis of reasonable belief. However the probability that something has occurred in contradiction of all past experience should always be judged to be less than the probability that either my senses have deceived me or the person recounting the miraculous occurrence is lying or mistaken, all of which I have past experience of.
This has some problems. For instance, my past experience may be lacking (obviously it is), or some events might be just unique but true.
However, what counts is the attitude, which I think is what works. While the Agnostic may be well too worried about the problems I've enunciated, in sheer practical matter, both would agree whenever anyone presented evidence of a God that it is
much more probable for it to be either an empirical error, an hallucination, bad interpretation of natural phenomena, or just a state of mental lunacy. Behaviorally speaking, both would never accept any concrete evidence of a God, rendering the question unanswerable.
But you see, there's always this nagging thought occurring in my head that I should just flatly deny / reject any unfalsifiable / unanswerable question. So perhaps to me the agnostic / atheist issue is not one of "technicalities" but of
social forms. I argue that we (4 so far) are all atheists in that sense.