I wonder how significant NYC is to SWA. Yes, it is no doubt the biggest market in the country, but there is an incredible amount of competition and JFK is not really a domestic airport. The value of JB JFK ops would be higher to someone like AA who has a lot of international traffic, as opposed to SWA who is a domestic carrier.
I really dont think SWA is capable of turning into an international powerhouse. Their IT is so far behind the times, and even if they buy JB they will have a serious amount of work to do before they can take full advantage of a JFK hub.