Today has been a week since I submitted my application, and had heard not reply. I found out mine was approved by logging into my NRP account.
People who submit instructor applications should receive an email to notify them if their application was approved or denied. Since these emails are automated, they sometimes get caught in spam filters. Anyone who has submitted an application can inquire about their status by emailing firstname.lastname@example.org. They can also see the status of their application in their account by going to Profile > Resuscitation Credentials and clicking the link on the right side of the screen "View Submitted NRP Applications."