According to the 1851 Census, Mary Pearce was born in St Luke's and was then aged 64, making her year of birth 1786/7.

The most likely baptism is the one at St Leonard's Shoreditch on 10th June 1787. The address is given as Hoxton Town and the parents are shown as James & Mary. The boundaries of both Hoxton and St Luke's seem a bit vague but parts of Hoxton seem near enough to St Luke's for Mary Pearce to have regarded her birthplace as St Luke's. Also this Mary's younger brother, William, was baptised at St Luke's.

Other Pearce/Pearse children baptised in the area born to a James & Mary around that time were Ann (1781 at St Leonard's Shoreditch), Edward (1783 at St Leonard's Shoreditch), James William (1784 at St James Clerkenwell) and William (1790 at St Luke's, Finsbury). All except James William are shown as coming from Hoxton (no abode is shown for James William) and James William was born only 9½ months after Edward so James William could come from a different family. James William was baptised the day after his birth whereas all the others were baptised 3 or 4 weeks later so I have not included him.

As to the marriage of James to Mary, there is the marriage of James to Mary Sharratt at St George Bloomsbury in 1778 and the marriage of James to Mary Goff in 1783 at St Luke's. If the marriage to Mary Goff had been a couple of years earlier then this would be a prime candidate. Did they, perhaps, live together as man and wife having 2 children before getting married?

I feel there is too much uncertainty to take this further at present.