It's difficult to know the timeline, but I got mine (no audit) within 2 weeks.
It's a good idea to move ahead and let your references know anyway so that they (and you) are prepared should an audit take place.
I have scheduled my PMP exam and received an email that I still may be audited. When will I know whether or not I will be audited. I would like to let my references know?
Training for Project Management Professional (PMP)®, PMI Agile Certified Practitioner (PMI-ACP)®, and Certified Associate in Project Management (CAPM)®