Does JFK immigration/customs let passengers with short connections bypass the queues?

From my experience short connection customers are not given any priority in any of the US airports (including JFK, although I try to avoid it usually so my experience is stale). You can ask nicely to be allowed to skip the queue and the CBP or the airport attendant usually administering the queue may or may not let you. It is your responsibility, not theirs, to book reasonable connections.

That said, recently major US airports upgraded their systems to use computerized immigration checks, so the queues may move much faster than they used to. For global entry it takes literally minutes, and you can try go that route, but the CBP person may still send your partner to the general queue. If they're nice enough they will send your partner directly to the CBP officer available next, which will solve your problem, but wouldn't count on CBP folks being nice. It did work for me once in a similar situation at SFO.