No, in that period, in England, if it was a Church of England baptism, it was most probably fairly soon after birth but not normally on the day of birth. (next century and after you quite often get months or years delay before baptism). Sometimes when a baby was sickly and might not survive, they were baptised at home on the day of birth, (the register then usually says something like privately baptised, publickly admitted). Very occassionally birth and baptism.dates are given in registers
The reference 'English Births and Christenings ' wasn't specific. I've improved that and changed certain to before. The 'source' is just an index we can't be certain whether or not there is anything in the actual. register to tell us more.