The marriage certificate won't - no parents names given on Tasmania marriages that early. Parents names I believe were not added until 1896 and they certainly are not on the two Tasmania marriage certificates I hold pre that period. Ditto death certificates for lack of information prior to 1897. After that you get place of birth (if known).
http://www.archives.tas.gov.au/guides/genealogyI think Tasmanian convict records are very interesting because they are more detailed than New South Wales re the treatment/puinshments, work on chain gangs etc of the convicts lives, but like all convict records, less for their genealogical details because Australian officals would be less interested in knowing that.
'In 1824 the British Transportation Act was passed, and it included a provision that there should be delivered to the contractor (or shipping agent) a certificate specifying concisely the Description of his or her Crime, his or her Age, whether married or unmarried, his or her Trade or Profession, and an account of his or her Behaviour in Prison before and after Trial, the Gaoler's observations on his or her temper and Disposition, and such information concerning his or her Connexions...'But by 1827 the Governor of Tasmania was still complaining about the lack of information being sent with the convicts from England "At present we stand in the extraordinary predicament in a Penal Colony of not being able to prove that the offenders transported from England are Convicts."
Certainly from 1827 onwards for Tasmanian convicts arriving you can get information from this source
'the Muster Master's duties was to examine the person of every Convict before landing ... to take down their description - History of their former modes of life - names of Relations, and connections, and the exact nature of the crime which they have been previously convicted of, and which led to their Transportation.' and Former Course of Life as may have come to the Gaoler's knowledge.....'which is much more helpful and detailed than for New South Wales convicts, but by 1827 the James you are interested in would have served at least 8 years of his sentence.
http://www.archives.tas.gov.au/guides/Con_guide.pdfStarting with records over here before pursuing Tasmania records which as I've said are very interesting in themselves and will give you far greater insights into James Betchley's life in Tasmania, but may not help you for his origins in this country, have you checked the Sussex Family History Society baptism index for possible candidates for James to establish a wider picture of possible baptisms in Sussex than that supplied by the IGI? As far as I know it isn't a county wide index for the period you are interested but it will cover some parishes not found on the IGI such as Hartfield for instance.
http://www.sfhg.org.uk/baptisms.htmlRegards
Valda
