Commutair
Your question is probably best answered by one of the people in the People Department. They probably would not give you a specific amount of time but they have said many times that type ratings make you more competitive.
Chase, who often posts on this board, has made the case on numerous occasions. You can search previous threads or PM him directly. He is a SWA pilot who is also an instructor at Higher Power Aviation (which I highly recommend to get your type).
My question is: how much time can you afford to wait to get the call? 6 months? 1 year? 2 years? I think that if SWA is your goal, you should do everything in your power to make yourself as competitive as you can. While a type rating will not guarantee you employment at Southwest, it may help to paint a Big Picture of your desire and commitment to become part of the SWA family. You can state that on an interview but obviously actions speak much louder than words. In my case, I didn't even think of it. My only question was when? I got it before I even met the minimums more than 2 years ago.
Good luck to you and your decisions.