The official answer is no. You need to clear security and you need a valid BP.
That said, I've booked refundable tickets a few times to get past the TSA there, most recently to
go to a concert. My main suggestion should you go this route is to pick a flight that is more than 3 hours out from when you plan to cancel. Once the flight goes to airport control getting unchecked in can be quite difficult and they cannot refund the ticket if you are still checked in. Also, you must refund prior to the plane's departure or your refundable value converts to a JetBlue credit.