The one time my family flew SW, we did not purchase EarlyBird (I just stalked the website precisely 24 hours before our flights to check in) and we were able to get low (early) numbers in the B boarding group and still find seats together. There was a family with 2 children (they looked to get at least 8-10) that boarded dead last (they must have checked in at the airport that morning or something) and they were unable to sit together at all. Flight attendants asked if anyone would be willing to move, but nobody did, and the kids didn't look anxious about sitting alone, so the family reluctantly went to the last four available seats, which were spread all over the plane.
I read up extensively on SW's boarding procedures before we left, and my impression was that in most cases, I think as long as you're willing to hover and check in at exactly 24 hours out (and so long as your flight is not a connecting flight from somewhere else, meaning it could already contain dozens of passengers before you even board), EarlyBird is not a necessity if you want to find seats together (or at least in pairs). If worse comes to worst and you are "that family" at the end of the C group, you'll just have to depend on the kindness of strangers.