In ireland at that time yes... a baptism record is a legal record.. you can get a passport with a baptism record and or a birth certificate..both are equally valid. (and when i applied for citizenship and a passport some years ago, a baptism certificate was prefered.. since it served as an independent legal document that was not controled by (US) government!-- i also needed a form certifying i was of good character, that needed to by signed by 1) local Police chief, or 2) Parish priest, or 3) superintendant of local School. i chose #3, since at the time i was active in PTA, and knew the local superintendant of the local school district.
also, at the time (circa 1920, and traditionally, as well) the mother did not attend the baptism. (mother's as a rule did not appear in public till at least 10 days after the baby birth) and superstition held that the god parents acted for the parents... that way, the devil/evil spirits wouldn't know were to find the child--all the better for his/her safe keeping!
