In Thomas Burkes and Ann Macnamara's marriage certificate from 1852 it says both of them are "free"? In Thomas' case that could mean a free arrival or a convict that has served his sentence and has a certificate of freedom. If FS had been on the certificate it would assuredly mean he'd been a convict? Ann Macnamara's age is 17 so even with the common 7 year sentence she would have only been 11 when sentenced and there no trace of a convict that young under that age?
Dennis Galvin was a witness at their marriage and he appears in a local police register for Ticket of Leave holders and their residences -
https://libraries.tas.gov.au/Record/Archives/POL515 I've attached the page and you can see he was at Captain Fenton's in 1849 but right at the end it says Thos Burk, F Forrest 9-1-54" This is Fenton Forrest the large property owned by Captain Michael Fenton -
https://adb.anu.edu.au/biography/fenton-michael-2038 So it would appear that Thomas Burke was a tenant farmer at Fenton Forrest in 1854?
The other witness was Susan Leary and I believe she originally Susan Mcauley who married Thomas Leary in Hobart in 1848 -
https://stors.tas.gov.au/RGD37-1-7p130j2k They both appear in the same volume as Dennis Galvin. Thomas leary was at Captain Fentons 28/8/'52 and Susan Mcauley/Leary was at Captain Fentons 15/4/'52. So you have most of the wedding participant's in one specific place? This leads to idea that Ann Macnamara may have been a servant to Captain Fenton in the same time frame?
