According to the U.S National Archives information page on U.S. passport applications (
http://www.archives.gov/genealogy/passport/#intro), a passport requirement for travel by U.S. citizens was the exception rather than the rule through much of U.S. history until the outbreak of the Second World War.
During the U.S. Civil War, passports were required travel by U.S. citizens for several months in 1861 and 1862.
Passports were required for travel by U.S. citizens during the First World War from May 1918 to the formal end of the war (by treaty) in 1921.
In December 1915, President Woodrow Wilson issued what is called an executive order
suggesting but not requiring that U.S. citizens travel with a passport.
It is only since June 1941 that passports have been required for travel by U.S. citizens.
The short answer to your question, then: The Massachusetts birth certificate would not have served as a passport for your mother. It only verified that she was born in the state of Massachusetts. Since it was issued by a state, rather than by the U.S. Department of State, I doubt that it would have been useful as a document for travel from the U.S. to other countries--to Ireland, for example. But it would have been useful to prove your grandmother's identity, place of birth, and citizenship/nationality.
An important question concerns her father? Whether or not he was required to have a passport for travel abroad would have depended upon the law in Ireland. Would that not have been U.K. law in 1915 and 1920? I don't believe that passports were required to enter the U.S. when he would have been traveling back and forth across the Atlantic.
Incidentally, you don't mention whether or not your grandfather returned to the U.S. and what ultimately became of him. I assume that he must have returned to the U.S., since you mention that the certificates are dated 1924 and 1929.
The two dates on the certificates are puzzling. One would probably have been the date of issue. But perhaps the embossed date is 1924 rather than 1929? You mention that it is faint. And it might have been distorted by the embossing stamp. Have you looked at it with a magnifying glass?
Regards,
John
