SW recently did a presentation at a job fair and was asked this type rating question. It was then asked back, "how many here have a 737 type rating?", a few hands go up, then "how many have experience flying the 737?", nearly all hands go down. They then went on to say they'd been working to get rid of the emphasis on getting the type. Noted that having a lot of 737 experience makes it hard to fly the SW way, and that its easy to revert to old habits. That most paying for the type get them in sims with different variants and procedures than SW, creating a negative transfer of learning. They worked on adjusting their training curriculum since they removed the type rating for those without it. In short, no isn't needed, and becoming less and less preferred if at all. My personal take is it may say something about your commitment, but outside of that they kinda like to train from a clean slate.