For what it's worth, I did exactly this a few months back. I arrived on a Delta first class flight from BOS (which had an international D1 segment prior) left my bag (a Rimowa no less) at baggage claim to go on a lounge hopping date with a lady I knew who happened to have a layover in JFK at the same time as me. I had a later AA flight that I did a free change to the next day to free up time and booked a night at the TWA.

We hit the Centurion Lounge, Chase lounge, Air India for a second after Virgin denied us, and the SkyClub before it was time for her flight to board her flight. That's when the real fun began, I went to the D1 lounge and they gave me no trouble. I spent several hours there basking in the glory before going to baggage claim in T4, retrieving my bag, and going to the TWA for a good night's sleep. If it wasn't for the limited time to spend with her, I think I would have taken my suitcase to the T4 luggage storage or my hotel first.

TLDR; I spent 4+ hours lounging around JFK on arrival and my expensive flashy metal suitcase didn't get stolen from baggage claim