It varies. I got mine about 2 or 3 days after my online status changed. Some get their letter before their status changes. Sometimes it takes a week or two.
My son got his before either of his statuses changed. The AF website changed the next day. Dodmerb didn't change until nearly 3 weeks later. Meanwhile, one of his friend's Dodmerb status changed the same day as his, and his didn't show up on AF's website for another couple weeks and he didn't get the BFE until nearly a month after that first change! Who knows?!