As jimbo99 says, if you have status it could be very fast. Since I've become Diamond all of my waitlists except for one have cleared within 24 hours. And the one exception took four days (I have a theory that whoever clears Diamond waitlists was on vacation/holiday and when they came back it was cleared first thing on a Monday morning).

They will not cancel your original booking until you are contacted and agree to the new date. If I were you, I would call a couple of times a week just to check.

If you want technical details on how their waitlists work, I can pass the details on. It could be a very long and boring post however.