I called Kim at SWA to verify that they received an extra form I had to send in. She told me everything was good to go, and that I'm officially "in the pool."
Having spoken with other guys who interviewed about the same time as us, it doesn't seem like SWA calls anyone to tell them that their background check is completed. Apparently, "silence is golden." I just happened to get more specifics because I called in for an unrelated reason. So, if you haven't heard anything, it's a good thing (no offense to Martha Stewart).