It’s only theoretically non searchable, IIRC each submitted document has to be OCRed every time a search is ran on the documents, and this is enough of a legal fig leaf to qualify it as not a registry. A sizeable GPU farm would make this basically a moot point.

Oh I agree. It is very likely that the electronic checks are recorded and could be used as a non-official registry of gun owners. I removed my comment to that effect because it is speculation. But, electronic records are so easily recorded that I have little doubt that the electronic checks are in fact an illegal registry.