You ask whether ‘in principle’ a neurobiological theory on religion could “account” for the experience of the believers. The answer depends on what kind of an account you are asking for and what you have in mind when you say ‘in principle’. If you mean by ‘account’, whether it could predict or even explain, I do not think so. We know that, at the least, we are made up of atoms. Your question, in terms of the kind of challenge it poses (even though the degree of complexity changes), is identical to the question: could a theory in physics, in principle, ever account for our experiences? What does ‘in principle’ mean here actually? There was a period when one thought, among other things, that it was possible ‘in principle’ to describe mathematics in a purely logical language. That is, many thought that mathematics has a “logical structure” and that, therefore, one could reconstruct mathematics aided by a suitably powerful logic. (It is called the ‘Hilbert program’, named after the originator of this research program.) Then a mathematician called Kurt Gödel proved that, in principle, we cannot even prove the truth of elementary arithmetic on logical grounds: even though we can generate true statements in elementary arithmetic (and know that they are true; they are called “Gödel numbers”), we cannot prove their truth. Nor can we prove their falsity. They belong to the class of “undecidable” statements. In other words, what appears obvious to many of us today, namely, arithmetic is ’logical’ in nature cannot ever be “proved”. This is an impossibility theorem that Gödel proved in the 1930’s. So, what we think is possible in principle turns out to be impossible ‘in principle’.
The lessons? Many, but here is one: as our knowledge grows, so does our understanding what ‘in principle’ means. Today, we would not know the things that a neurobiological theory has to do; we know even less about what a neurobiological theory of religion has to do. We do not know what it means to account for ’experience’; we know even less what ‘religious experience’ is and what requires accounting. However, we know enough to say the following: for any time in the foreseeable future, there will be no neurobiological theory that can account for (explain, or whatever else) “beliefs” of any kind. For the next hundred years at least, there will no neurobiological theory of ‘beliefs in superstrings’ any more than there will be a neurobiological theory that explains the belief that “Bible is the true word of God”.
If you are interested in this debate, I suggest you try to read up on the ‘reductionism’ debate in the philosophy of science and philosophy of psychology/philosophy of mind. The matter is far, far more complicated than what I have said in the above two paragraphs.