I submitted with mine, have you received an AOR yet? if yes and they need something they will let you know, if you have you not received an AORI yet they might send the package back.
how come you don't have the birth certificate, you should try and get one and email them with the copy asap.
Birth certificate as such is not mandatory, if you home country's government doesn't issue them, but some sort of government-issued proof of birth is. I'm from a country that doesn't issue birth certificates, so I sent an equivalent document issued by the national registry that contains the required information about me and my parents. And that was fine with CIC.
You should ask your home embassy or consulate if there's something else they can provide you with.
But if you do have a birth certificate but you just don't have access to it (lost it and getting a new one is too hard, or whatever) then that's a different issue. Either way CIC does require proof of identity of this sort.