Hi Bg,
I am under the impression that the beneficiary's birth certificate is
100% necessary at least by the time of the interview. And, if I'm not
mistaken, I'm pretty sure they will also want to see the original of the
Petitioner's birth certificate as well.
This was the case for us, anyway. I am just now finishing up Packet 3
in preparation for an interview date for my fiance, and both of our
original birth certificates are required documents (copies sent to the
consulate ahead of time, and originals to be presented at the
interview).
If I were you, I'd get started obtaining the birth certificate ASAP.
Best Wishes!
Rene