I assume it says his parents are William and Margaret Burns nee Dunlavy?
Although you have his birth certificate it doesn't help with whether he went to the USA.
At Reply #14 Jon found this:-
Doesn't mean that either William died then of course, but on FreeBMD there's only one William Burns death in Chester le Street district from 1911 until 1938 (when it was abolished)
March 1924 Chester le Street 10a 833
Burns, William
age 22
Out of sheer curiosity I obtained a pdf for this death and it says the following:-
Where & when died:- Fourteenth January 1924 E.22.D Elisabethmills, Birtley R.D.
William Burns, male, age 22.
Profession:- Colliery Rolleyway man (below surface)
Cause of death:- TB and exhaustion
Informant:- William Burns, father, present at the death, E.22.D Elisabethmills, Birtley
As you can see the E 22 D corresponds with the electoral register info that Jon found.
Autumn 1923 sees a change.
Polling District C. Parish of Birtley.
Burns, Margaret (residence) E Sec. 22D
Burns, William E Sec. 22D
Burns, William (Junr.) E Sec. 22D
To my mind this would mean that whoever went to the USA it wasn't William.
In family history one has to accept the unexpected - his other brothers will need to be investigated to see where they went. Memory is a wonderful thing but it is not always reliable especially after a long period of time.
A small example from my family history - my mother always stated that her grandfather was one of twins. He wasn't and I have birth certificates to prove that. So her memory was at fault there.
You will need to find out if William's other brothers went to the USA and if any of them married there.
If you would like a copy of William's death certificate, send me a pm with your email address and I will send it to you.