It doesn't take long to process a membership. I believe I received a response back via email within 24-48 hours of me submitting my request for membership. I also received notification and confirmation of my application via the US Mail within that first week. The first letter I received thanked me for my membership request and explained the next step, which does take awhile longer and can be as long as 30 days.
Every new prospective member must be presented to the full membership before their membership can be considered full and active. The names of every new prospect are listed inside of the Linking Ring publication that is sent to all active members. This allows all members the chance to review that list and object to anyone on that list that a member feels are unworthy of membership in IBM. Maybe a member believes that this prospect has violated "the code" or presented themselves or magic in a manner contrary to what the brotherhood and/or it's members represent OR for some other good reason that compels a member to raise their objection.
I'm sure that any prospective member who has received an objection to his membership request would be given a sufficient time and space to answer, respond, and defend those objections, which could extend this "processing time" even further.
I don't know if this answers your question or not. Normal processing time is quite short and quite painless. Have you already submitted your application?