And this would effect Conneticut only. Your mention of you having the abiility to make an FOIA request seemed like you where talking about this in a federal sense.
Also Dan mentioned redirecting NICS to check no fly list. The EO mentioned in the OP has nothing to do with that either.
"We" in the general sense. Now there's another reason to push for due process w.r.t. the lists. The EO specifically calls out using federal lists, but not at the NICS point, at the FOID point.