Not unless Mexican law permitted it and I doubt that Mexico recognized anchor baby citizenship in 1908 or today, unlike its loony neighbor to the north of it.
A strict reading of U.S. v. Wong Kim Ark would reveal that the U.S. didn’t recognize anchor baby citizenship either ... at least not until the Immigration and Nationality Act in the 20th century, which may have some loopholes. Otherwise, the court said that the 14th amemdment only confers citizenship if the parents have permanent residence and domicil ... which means the parents had to have been legally admitted into the country as permanent residents.