For what it's worth, I dropped by the CFO's shop on Jasper Ave here in Edmonton about a month ago and spoke with a very helpful person.
She tells me that perfect online applications should be able to count on a six-to-eight week turnaround from submission to receipt of the license in the mail. She reminds us that if the app is perfect - t's crossed, I's dotted, clear pic on a plain white background, references in place, etc. - AND the application is done online, they should have it in your hands in a month and a half tops.
Errors in the app slow the process. Paper applications slow it up even more, doubly so if there are errors. You mail in a problematic app and they send you a letter requesting clarification. Your app goes back to the bottom of the pile while they await your response, also by mail. Do it online and they ask questions by email, which should be faster than awaiting Canada Post.
Your mileage may vary, but this timeline is the one I'm giving people who take the course with me.