If you want to check out that death in NSW you could get the death cert, which should state his birthplace, occupation and parents' names (if the informant was aware of them). It should also say how long he'd been in Australia.
It's cheaper to get a transcription from an authorised agent than to buy a cert:
http://www.bdm.nsw.gov.au/bdm_fh.html#transcription
There are some Aus censuses online (mainly 1891 and 1901), but the only person named is the householder.
Ancestry has NSW electoral rolls, but only from 1930, although I think there may be some earlier ones on FMP.
Ancestry has Sands Directories, which show a Thomas W Hayden in Clyde Street, Granville in 1910 and 1915 and in Albert St., Granville in 1919. Unfortunately it doesn't give his occupation.