I'm curious too. I think it depends on the date the state board has the (monthly?) meeting where license applications are reviewed. This might be on the BOA website calendar, and then the paperwork needs to be in their hands a certain number of days before this meeting (sometimes 10 days). The whole process is probably way different for every state though, so I'm not sure.
I was wondering myself as to whether you're allowed to send in the license application before receiving a congratulatory letter. Jeff says in his 50 things to know about the CPA exam that you can do this (step#45). http://www.another71.com/50-things/ "Fill them out, write a check, and mail it in. Donʼt wait for them to take their sweet time in sending some packet to you. Chances are you can send them the forms and get the process rolling before they even slap the postage on your envelope."
And candidates in 3 different states have done this and have said it's fine (I gotta check my state though), but that should speed the whole process along.
REG 68 (2008), 82 (2010)
BEC 79 (2010)
FAR 81(2008), 88(2011)
AUD 82(2008), 95(8/31/11)....DONE