The problem is that this child when he/she becomes an adult and not having a birth certificate or a SS# i believe can cause many problems.

Wont be able to leave the country
Wont be able to get a job
Wont be able to buy a home
Wont be able to buy a car
Wont be able to have a credit card
Wont be able to get any sort of loan
and the list goes on!

Just about everything, i believe requires a SS#

I also think that the child will not be able to attend public schools or college.