Will a book become divine merely by way of its own claim of being divinely inspired?


No. Any book which lays claim to its own divine status must necessarily prove that it is, indeed, divinely inspired. However, on the other hand, it is of primary importance that if a book is of divine origin, it must, of its own accord, or by way of the messenger who had come with it, raise that claim. In reality, none has the right to claim divine status for a book unless and until either the Book itself or the person who came with it makes that claim first. If, the followers of the book, then, say that it is of divine origin, it will be but their witnessing to the truth of the claim already made by the book or by the individual who had come with it. But if that claim itself is not there, any witnessing to that claim is obviously irrelevant.

This is the case with all the other religious scriptures apart from the Qur'an. None of them has claimed divine origin for itself. In fact, it was their followers who conferred on them the status of divinity. As of the laws of dialectics and argumentation, this is but a gross anomaly; a thing so irrelevant as to be unworthy of consideration by the intelligent. It is to be dismissed as simply as the witness who appear in court for the proceedings of  a case in which there is not the very subject of contention itself.

This, however, is not the case with the Qur'an. It itself declares that it is of divine origin. As such there exists a claim. What remains to be seen, then, is the veracity of this claim. Indeed, there is meaning and substance in such a verification. This is quite unlike the futile and pointless scrutiny of the divine origin of books which make no such claim in the first place.