No nation is without sin, so...yeah, I can see it happening. Don't get me wrong, I think Mexico is already viewed as North America's premier power that isn't the United Kingdom. But I could see it long term, being their ticket to be recognized as one of the world's great powers.
I feel like in ttl there won't be a unipolar or bipolar world. It'll probably have the old paradigm of major great powers and regional powers. In the case of North America however I feel like rather than Mexico being the premier power, once the US gets its act together, North America will probably be a multipolar area. The Commonwealth and New England would be the middle powers comfortably staying neutral while likely playing off each power for their own financial gain and national security interests.
While Louisiana would be grateful for Mexico's aid, I doubt they'd want to be a quasi-puppet state of Mexico like how New England for the British. Plus with their control over New Orleans, they'll probably have a large economic and agricultural center. As the Mississippi River is one of the most navigable rivers in the world, control over it will make the country and cities like New Orleans and St. Louis fabulously wealthy. Though with the continued French culture in the region, you'd probably see some interesting variations of French culture develop. Some stuff might end up going to France and becoming popular there.
Yeah but its been largely targeted on Catholic area's like Italy and Ireland. The tidel wave of WASP's probably isn't in their interests.
WASP? What does that stand for?
Still a more Catholic North America is honestly quite interesting to be honest. Plus without the chaos in Mexico and the regime of Benito Juarez and his anti-clericalism, Mexican society will probably have the Catholic Church as a major political force. While not officially part of politics it probably will be another pillar upon which society and government functions.
As for Napoleon II, him as a "Mayan King" does sound interesting. It could honestly work as something akin to the constituent Kingdoms within the German Empire of otl. Though Napoleon II might not accept such a proposal. Technically Napoleon II is the senior member of the House of Bonaparte as he's the only son of Napoleon, and the current claimant to the Imperial Throne.