This is true. Fairyland originally didn't send out any certificates with their dolls. So, you will find some of the older dolls without the CoA. It's also true that some of their dolls don't have their sculpt names engraved on the inner part of the heads either.
No, the CoAs were only started in like 2014 or 2015 if I recall correctly, before that no CoAs were included.
My FL dolls don't have COAs either. I actually checked with them before about it, and this is what they replied:
Keep in mind that when they say orders placed, many dolls received in early 2014 were ordered before the CoAs started being issued so they still wouldn't come with one.