Hi,
I cannot see a convict application to marry so appears he wasn't married by the time of his CP.
You say he died in 1880 Sydney....is this the death you mention?
5884/1880 BURTON JOHN AGE 74 YEARS DIED BURROWA

You could purchase a copy of his death cert and it should tell you if he was married or had children. Using a NSW Transcription Agent (just google) is cheaper and quicker than purchasing via NSW BDM.

Kellie