I agree with some bits of that, and disagree on others.
Overall, I would say that I am in general an agnostic. In theory, there are infinite possible gods, and of those infinite possible gods, there are again infinite numbers of gods that can’t be proved or disproved one way or the other using any of the tools we have at our disposal. I think that in the most general terms, the only reasonable conclusion for all people, whether they consider themselves theists or atheists, is that of general agnosticism, on both those grounds, the concept of a random universe, or just pure potential inability. And of course I don’t believe we can ever disprove or prove anything, so when I say “prove” or “disprove” further on, take it as for a certain value of proof. 
That said, I disagree that a being defined as supernatural in nature cannot be studied using the tools of the natural world. Certainly this is true of a being that does not interact at all upon the natural world; a being entirely seperate, a deistic god, is entirely unprovable or provable with science or logic. A problem with that is this; an entirely supernatural god can only be observed using supernatural methods, and thus those who are believers must accept that a part of themselves is supernatural in nature (and I would think most do). Yet we may study them, and us atheists too, if the supernatural part of our nature is extended to us also. We can study those parts of us that exist and affect the natural plane. If a god, too, is not only assumed to be supernatural in nature but also to have had some impact on the natural world, then we may certainly observe those happenings.
Now, you may say that doing so doesn’t actually disprove anything about the god itself. A miracle of an apparent picture of a holy being discovered in a cave, for example, might be discovered to have been carved there by humans instead. That doesn’t disprove the god; only gives an alternate suggestion for how it might have come about. If the claim is “This could only have come about through a miracle”, then that claim may be disproved, but not the god.
But actually, we can disprove a particular god with that natural conclusion; we can disprove the existence of a god who brought about a particular event that could not have happened any other way. About the existence of a god who may not have brought about the event, it of course says nothing other than providing the alternate solution.
So natural tools can in fact disprove gods; specifically, if we can come up with alternate, natural suggestions for how events may have occurred, then any gods for whom it is suggested they alone could have caused the event are disproved. To use an actual example; should the theory of evolution be accurate, it does not disprove the existence of a god who may or may not have used it. Likewise it says nothing about a god who planted evidence to lead us to such a conclusion. However, a god for whom the creation of creatures could not have happened any other way than spontaneous creation is disproved; all that is required there is the alternative explanation.
Thus the question for me is; does the Capital G God include in its definitions anywhere the clause that something it has done could only happen because of that, and in turn can we come up with alternative, natural suggestions? If it does, and if we can, then it as a concept is certainly disproved.
Thus we arrive at a problem. It’s been suggested that the definition of the Capital G God includes that of “scientific method cannot disprove it”. Now, it is possible that this particular God also includes a definition of the type i’ve suggested above; one of “there are no natural alternative explanations for this particular thing this god caused”. Since theoretically the definition of the Captial G God could include this other definition, we can’t rule out in each and every case that scientific method cannot disprove it.
Now, it is possible the opposite is true; the overall definition of the Capital G God does not include the no-alternate-natural definition. However; if we say that the Capital G God cannot be truly defined in such a way, we need to be able to say that there is no chance that it may embody this definition supernaturally - but also that it cannot embody that definition naturally, either. And that itself is a no-alternate-natural definition, and as such is theoretically actually disprovable.
Thus we cannot say for certain that the Capital G God cannot be disproved by scientific method; either it encompasses as part of its defined nature the idea that it causes events that cannot have happened any other way, theoretically disprovable by finding alternate natural causes; or it does not, in which case accepts that it does not encompass that as part of its nature, which includes it encompassing it naturally as well as supernaturally, and so brings in the element of theoretical disproval anyway. So IOW, no, we can’t say that.
I think. Reading back on that lot, i’m sure there are plenty of holes in it, but i’m too tired to see them. 