Child birth certificate?

[heo luoi 206]

Im a viet-american (both my parents are viet but I was born here)
My wife is a viet national.

Our child is due in DEC

Should I pursue?:

4. BIRTH REGISTRATION AND PASSPORT FOR US-BORN CHILDREN

Record in the birth registration book

Children born in the US to Vietnamese parents (who have valid Vietnam passport); to parents, one of whom is not Vietnamese and whose birth certificates have been issued by the US relevant authority, can apply for Vietnamese birth certificate and passport.

http://vietnamembassy-usa.org/consular/vietnamese-passport

Agreement on child’s nationality (signed at and notarized by Public Notary) if one of the parents is a foreigner (does not bear a Vietnam passport).

I am pretty sure the US does not recognize dual citizenship. I don't know if this would be advantageous for our kid(s) to be included in the records over there? I certainly do not wish to denounce their US citizenship.

In the form states;

" Fully agree to choose Vietnamese Citizenship for our child:"

Anyone done this?