I did have another think on this over the weekend. I am doubtful whether you will solve this by online research only. It would be useful to search the parish registers for a baptism for Thomas Williams the problem is which registers would you need to search (or have searched). I reckon Llanwrst would be a good start, followed by Conwy and Rowen, possibly Caerhun. You would be the best person to decide which places to look at as you have by far the best knowledge of the family.
The information you have on Emma is corroborated by census returns, death certificate etc. Since the 1851 census shows her to be a widow, I think I would accept that which means you need to look for a burial, or death, for Thomas prior to that. He is missing from the 1841 census too, that didn't require people to state their status, so it is likely he had died before that. He would have been alive when the children were baptised so the period in question is 1817-1841 (possibly 1851). I reckon Llanwrst would be a good place to look. I have attempted a search on Ancestry and Find my Past but nothing shows up for him. It it possible the parish registers of burials haven't been transcribed as yet for Llanwrst, or other possible places.
I suspect Thomas's age would be quite near to Mary's and c1770-1775. I note Mary's age wanders a bit, 76 in the 1851 census and 88 in 1860. Ancestry shows her baptism as being in Caerhun on 29 March 1775, "Daughter of Edward Evans of the shoemaker by Mary his wife".
I think the best bet would be to try and find his death, or burial, and work back from that.