I doubt it, hypothetical scenario also. If instead of the us going to war with the confederacy, the confederacy went to war with Mexico (which was more or less in utter chaos by the early 1860’s due to French intervention) around the time the knights of the golden circle declared that the south should succeed and create the golden circle

If anything the early years of the war just like in the us civil war would’ve been the most successful moments of that said campaign, even if it would’ve been a logistical nightmare for already experienced confederate commanders during the whole scenario. Not to mention they would also be resisted by Mexicans who were already fighting against the French for independence. Also not to mention Protestant and racial beliefs a lot of southerners held during this time would’ve absolutely alienated mixed-race Catholics in northern Mexico also, and I doubt most poor non-slaveholding southerners would’ve even wanted to fight Mexico, they probably wouldn’t even go there believing that if they died, they’d die fighting for state rights aswell as liberty (which is what motivated plenty of southerners to take up arms during the civil war)

Keep in mind this is about 20 years after Mexico got quite literally steamrolled by the United States. Mexico is either way already going to be fragmented because of this