Seems to depend on the DAME. Some are really good at getting everything correct up front, others takes days/weeks to complete the submission/coding process, then it takes CASA even longer. Also, will take longer (maybe much) if there's anything "unusual" which has to go to the CASA medical specialist - even if it's not a problem - just getting through the specialists' paperwork queue takes weeks!
I've had them take many weeks, but the last couple (different DAME) when through almost instantly!