I sent in an affidavit instead of a birth certificate. However, my wife is the primary applicant and she has send in hers. Unfortunately, I would stop short of assuming that CIC might not ask for a birth certificate even after the AOR is received. The visa officer might want it. The truth is we just can't be certain to be honest. Ofcourse there is a likelyhood that they might not ask for the B.C as well once the AOR has been send in todays circumstances. Ie, after the closure of buffalo office, I think the AOR as well as the file number is being send from the Sydney office. Just to be on the safe side, it wouldn't hurt to arrange for an affifavit and send it the visa office if you haven't already. Something that I would do. Cheers.
