So, it's possible for them to hold the NICS check without holding the person data. NICS is identified by a transaction ID and, at least as I understood it (NICS is an FBI system, so we had limited insight from the ATF, and as a contractor, I had possibly less insight than an ATF agent proper), the PII (Personally Identifiable Information) is purged from the NICS check upon completion of the check.
There might be, and probably is (at least) a record of the transactions that were processed and the result of the transaction. Also, as I understand it, if the check fails (hence, no gun is disbursed), then the PII may be held longer to aid potential investigations.
From the ATF's perspective though, PII definitely isn't kept, or at least wasn't as of 6 years ago. I honestly don't remember the specs on failed checks. I don't think that it did, but that isn't to say that if they are prepping for an investigation of an FFL that they couldn't requery the FBI for more thorough NICS records than what they hold in their own systems.
That's good information on the NICS records. It would seem, though, that given the information in the NICS check record and information attainable from a mandatory bound book inspection that the end result would be the personally identifying information of the transferee. It is good, at least, that this would necessarily be a manual process.
I've always thought that the most querulous position the ATF has taken was on FFL closure. If an FFL closes up shop for any reason, they must ship all their records to the ATF.
I don't have any personal insight into what happens to them after that, but it seems like at least a sparse, time-delayed registry could be built from those records... which is perhaps the best kind of registry as private sales would skew the data substantially.
If true, clearly someone would have to be holding NICS records and the ATF would have to have access to them.