I may be mistaken, but...
I think the CAF stands alone, and once you submit it, your school can start scanning in your LoRs.
Programs understand that LoRs are still arriving, so you might want to just assign the letters now (if you know which ones go to where) and not worry about it later. Check with your office, though, to see if your letter-writers need prompting.
I was able to make corrections and different versions of my PS after submitting my CAF.
Hope this helps!