I interviewed w/o the type, got hired, then got my type. Interviews have started up, and requirements have not changed--type is only required to start training, not get an interview.
That said, I would suggest getting the type now if money is not a factor. You will definitely get called quicker for an interview. Biggest advantage from the company's standpoint is that the more guys with a type that they interview and subsequently hire, the more guys that are available for training ASAP. With the pool being drained quickly, SWA wants to hire as many guys/gals w/types to make sure the training pipeline is not interrupted if classes continue thru the end of the year. And all indications are that this is the case.