James,
I have almost completed the process. I put in my application on 22nd January, sat the first tests on 14th February and found out the results eight working days later. After that, if you're successful, you have to attend the final assessment within three weeks so i sat mine on 14th of this month (Tuesday) and then found out I'd been successful on Friday! Still waiting on a formal offer, medical and security clearance but in essence it's taken me two months to go through the process.
I would have thought if all goes well you should be able to get through before you go away; but then if did - would you really want to go away?!
Hope this helps, Rob.