No, of course not. There was no immigration from India to Britain in the 1700s. Their surname was probably Parnham anyway, as in Henry's marriage record.
Looking for Henry's birth, there is a candidate born nearby in Flintham who would be worth investigating.
First name(s) Henry
Last name Parnam
Baptism year 1705
Baptism date 27 Dec 1705
Denomination Anglican
Place Flintham
County Nottinghamshire
Country England
Father's first name(s) Will
Father's last name Parnam
https://www.findmypast.co.uk/transcript?id=GBPRS%2FNOTTINGHAMSHIRE%2FBAP%2F000588245
Flintham is about five miles from Sutton-cum-Granby which is a point in his favour but, on the other hand, Henry and Sarah don't seem to have named any of their sons William which would be unusual.