Takes about a week for Apple to review and approve an app assuming that they don't have any comments.
The App approval may only take a short time, but MFi approval can be an exquisite experience. If the iPhone app is going to use Bluetooth 2.1 + EDR (and not 4.0/LE) to be compatible with iDevices before the iPhone 4S, one must jump through the MFi hoops. It can be a real, agony producing, pain in the a$$. I know of one project that was put into the "exception" program where the project was not approved and not denied -- and there it stays for the last year. Cute, no?