I wouldn't have thought that Jetblue (B6) would interline bags. I fear that they are much like Squeezy Jet in that resepect. They stand alone, basically, and won't do anything relating to another carrier.

This then answers your next question - you'll have to exit anyway to get your bags so you are just as well going to the check-in desk to get the boarding card and to drop your luggage.

Someone might prove me wrong, though!

Oh, and hope you're well K!!!! Hope you're Christmas and New Year were excellent!!!