I want to say signup confirmation takes from 24-48 hours. Sometimes it can take a little longer, and that just means you caught someone at a bad time. I'm pretty sure new members applications are reviewed one-by-one, by hand...err, eye.
If it take a really long time to get anything back (4+ days) you should probably visit the SWC Problems Board, and let someone know. There may be some extenuating circumstances preventing applications from going through.
ou should get either an accepted email, or a declined email. The declined one should explain why it was declined.