The answer is that probably I do have a connection in that if he had a sister Sarah then she was my wife's 4GGrandmother.
The difficulty is in deciding who were the parent's of these
children. You do not give a reason for your enquiry, but you may, like me, have some difficulty in working out the Baynes/Baines family. They were mostly named as Baines in the register up to 1812 and Baynes after.
You give a date of birth c1800. There were two baptisms near that time, 1802 probably 29 Sep. but not clear and 7 Oct.1804, both of these are given parents John & Mary. There is no burial in the intervening period so do they have different parents, or did one die without it being recorded?
A John Baines married a Mary Hall in Radwinter 1 Nov 1793. I think that this John is probably the son of a Thomas and Ann Baines and was baptised 3 Dec.1775. A John Baines also married a Mary Rushforth in Radwinter 13 Dec.1774. As I can see no burial for a Mary in between I assume that these were two separate couples.
There was a steady stream of baptisms in Radwinter of children to John & Mary from 1775 until 1815. You can assume all those before 1793 belonged to the elder couple, but can you assume that those after all belong to the younger. Looking for a baptism of Mary Rushforth again there are two possibles, 15 Nov 1747 and 26 Aug.1764. If she was the first then she has to be too old come 1800 to be the mother of a John. If the younger then if she was baptised as an infant then she was too young to marry in 1774. If however she was baptised as a young girl then it is quite feasible.
Perhaps you would now give me your thoughts and rell me your connection.