The thresholds for antibody tests were established using known true negative samples (e.g., blood banked before the pandemic) and known true positive samples (e.g., patients who tested positive by PCR). But patients with worse symptoms are over-represented among people who tested positive by PCR (since they're more likely to seek a test), and patients with worse symptoms will generally have higher levels of antibodies in the blood. So if anything, the sensitivity of the test is probably an overestimate, which would make the number infected an underestimate.

I've seen a few papers testing asymptomatic patients (identified by contact tracing or other mass testing), with mixed results. NYC uses an in-house test for which I don't believe any paper exists, so I don't think we can say anything there. The IFR from NYC's serology is higher than most other estimates, which could imply under-ascertainment but could also be real (e.g., because they forced nursing homes to accept positive patients, because they were doing early intubation that we now know is harmful, etc.).