There are no PYCROFT baptisms at Stoke Damerel 1801-1817 I'm afraid. (My transcriptions were made from fiche of the original registers)
There were 2 burials at Stoke Damerel: Thomas PYCRAFT 3 Jan 1808 aged 8 months and Eleanor PYCRAFT 13 April 1810 also aged 8 months.
An Elena PYECRAFT was baptised at Plymouth Holy Cross, (Roman Catholic) 24 September 1809, born 5th September 1809; dau of the 'lawful marriage' of John PYECRAFT and Margaret his wife (alias DONEVAN), living at Dock.
John & Margaret PYCRAFT also baptised a daughter, Mary on 20 June 1800 (born 16 Jun 1800), at Plymouth Holy Cross.
So, it's possible your family were RC and possibly of Irish origin as the sponsors were Timothy SULLIVAN and Ann BURGESS.
Looked a little further and found a James SYEROFT (as transcribed). The actual register reads: "On the 24th April 1803, I have baptised a son named James, born on the 20th of the same month, of the legiticum (?) marriage of John PYCROFT & Margeritte, his wife (alias DONEVAN), residing at Dock. The sponsors were Cornelius DONEVAN and Brigitte READ.