It can be anywhere from a few minutes, to a few hours, to a few days, to a few weeks. I've even approved patterns months after they were submitted.
but we only accept a very small percentage of patterns right now, so it will probably not be approved at all.
I'm trying to change that, see: http://kandipatterns.com/questions/97/pattern-uploads-let-users-vote-for-which-are-featured-on-the-site