It can take 24 to 72 hours for Apple to process the submission, in our experience.
Update: May 2018
We have observed significant delays in Apple's processing of podcasts—as long as 10 days. Shows are being processed, and some very quickly, but others are taking considerably longer than usual.
Update: November 2019
Due to a significant increase in podcasts that require approval during the holiday season, please expect an extended approval period for any shows submitted to Apple during the holiday months.