I am not related - but I had a few minutes this morning to look at your question - heres notes on what I found
The marriage of William Silvester & Rebecca Jackson was in 1852 from the IGI - William age is 22 and Rebeccas is 18
from this I found a likely Rebecca Jackson in the 1851 census at Draycott, Bourton on Dunsmore - next door but 1 was Thomas Sylvester and his family with son William who is also the right age. Rebecca is with her grandmother Elizabeth Warren aged 76 born Glous Gifford, and staying with them is visitor John Stokes aged 11 born Coventry.
A likely baptism for Rebecca daughter of Elizabeth Jackson 15th January 1837 Bourton on Dunsmore.
from Free BMD a marriage for Jesse Stokes June qtr 1839 Coventry with one of the possible brides Elizabeth Jackson
from the 1861 census you found Elizabeth w/o Jesse Stokes was born about 1811 at Draycott - there is a baptism 12th Jan 1812 Draycott of Elizabeth d/o John & Elizabeth Jackson, I suspect that John died sometime before 1822 when there is a marriage in Bourton on Dunsmore of William Warren to Elizabeth Jackson.
Therefore yes the Thomas Silvester with Jesse & Elizabeth Stokes in 1861 is very likely the son of William & Rebecca. To prove it further it would be ideal to find the death of John Jackson in Bourton and check that Elizabeth was a widow at her marriage to William Warren in 1822, but as I am working mainly from the IGI I don't have this info. If you bought the marriage certificate for William & Rebecca it should give their fathers (or lack of them in Rebeccas case).
I hope all this makes sense

Debbie