After you have sent the paperwork, call them after 2wks as it will of been assigned to someone and they will tell you if you need any extra documentation that you can fax or email through to them. Ask them directly if there is anything else they need or needs to be updated to help the process along and if you have a good one, they will tell you straight away. If you have needed to provide updated or more documentation, call them in a weeks time (so they don't feel harassed) to make sure the documentation was up to standard and how everything is progressing. I did that and got told (after providing some more info) that it had been approved and around 8 working days the money is in your bank account.
Make sure you are friendly and act like you are trying to help them do their job. The rate of applications have increased significantly since people have realised you use super for WLS so they may be a bit short and unhelpful as feeling overwhelmed with workload. Don't take it personally, just turn around and say, is there anything I can do to help you to make it easier to process and they will appreciate a response like that.