for me, it actually took 1 business day, I submitted oct 20 or 21. I would say that you should probably be fine..4 weeks is the outer limit of how long it would take, but lots of people are saying it took them less than 2 weeks.
Also, some deadlines are for the date that you need to have submitted your application into OTCAS, and some deadlines are for when you must be verified. So if it's the date you need to submit by, then this won't even be an issue. But either way, I'd say you're probably fine