Nothing in versions of "General Taylor" suggest any connection with Los San Patricios.
There is nothing besides the name General Taylor, and the verse in some renditions from the spiritual "Mary Wore Three Links of Chain" or its occurrence in the secular song "Old Blue" and others (probably a floater or filler, added to songs from the late 19th century to mid-20th century) to suggest a date. The relationship to the mythic "Stormalong" character of the shanty is possible.
The truth is, we have only supposition about the age or authenticity of "General Taylor."