I find that highly unlikely since the Dept of Health had ALL the birth records. A news person would just go to the D of H and get all them to put in the paper.
The first laws requiring reporting of births and marriages began in 1842, but many of those early records have not survived. In 1896, the Department of Health was given the responsibility for registering births.
The Department of Health has the following records of birth: Hawai'i: 1877-date Kauai & Niihau: 1896-date Maui & Molokai: 1896-date Oahu: 1863-date
From 1911-1972, a person born in Hawai'i but whose birth was not registered could apply for a delayed certificate, commonly known as a Delayed (Hawaiian) Birth Certificate. Births prior to 1911 are included, and all of these records can be found at the Department of Health.
HWST 115 - Mo'okū'auhau: Hawaiian Genealogies: Birth Records
Most newspapers, especially the Advertiser that appeared in, don't do it. They wait for family to send in announcements. Also legal notices are "filler" used to fill space that is not taken up with advertising or news and if there isn't enough space, left on the editing room floor. . . and will never get published.