SWA changes with the tide - if you are in a competitive hiring environment then you'll probably find that having the type is necessary for interview. They always require the type for hiring, but relax the requirement for interview if they are finding it tough to fill their interview sessions with those how already have it.

Since this type requirement is such a well-known fact, all airlines are savvy and will look for it on your resume or ticket. Every employer out there wants to know you really want to work for them (it's all about ROI, my friend) so they will inquire if you have obtained it. This certainly doesn't mean you won't get the "other" airline job, they know the score and the competitive environment. You'll just have to be a little more convincing that you won't jump from their ship once SWA starts hiring again or invites you to interview.

Hope that helps