I don't know if JFK is different, but I was in a similar situation last week in SJC. When I got to the Admirals Club, I had the AAngel call down to baggage claim and had them pull my bag. When I went down there 3 hours later to pick it up, I gave them my last name and flight info, and a guy went into a back room to bring me my bag. Fairly painless...

(Now, what I don't know is if my bag just sat on the carousel for a while or whether they actually pulled my bag before it got to the carousel.)