Both Thomas & Hannah's signature are in the same handwriting of the details of the marriage ie the person that filled out the certificate also filled in their names as signatures. Yes the NSW BDM was reconcile with the church register. Details on children's birth certificate were given verbally. They were married at St Stephens, Church of England Newtown. I might add that Hannah was 2 months pregnant so the wedding was hurried.
If it is all in the same handwriting, then I suspect that the reconciliation was not fully fully complete (sometimes five registers needed).....

first babies can often be in a hurry but that does not stop the clergyman from recording all the information. In the 1870s there was a huge dispute between the NSW parliament and the Churches re just how much information to provide to the 'secular' BDM offices. But the C of E clergymen recorded the details about the parents on several registers at the local level.....
It is a matter of getting to the original one to see exactly what was recorded re Hannah's parentage to learn further about both her mum and her dad.... I also find it a tad co-incidental that Mary's surname becomes ROELS, and that Hannah's dad was John Philips .... and there's a Philip John ROELS in Newtown when Hannah Sophia marries there.
http://www.ststephens.org.au/ I think their older parish registers would be with the Diocese, and if that is so, then there's some good news
http://www.archives.anglican.asn.au/index.php/p2/family_history "We are currently planning a mass digitization project with Ancestry.com which will provide even wider public access to the information contained in our baptism, confirmation, marriage and burial registers."
If my memory serves me well, it was Dundee who first alerted RChatters to the above news

Cheers, JM