I remember from the Issac Deutscher "Prophet" biography of Trotsky is that he was almost put on a boat for Havana instead of New York. Trotsky tried to avoid this at all costs, he felt New York was a much more important place for him to be.I could picture a TL where he finds himself in Mexico in 1917 instead of New York. He may have had some influence on the Mexican Revolution but I doubt it would have been enough to make a major difference.Perhaps in the 20s there might evolve a Trotskyist inspired Mexican communist party which might influence subsequent events.
Yes, he tells this story in his memories. In 1915 or 1916 (I don't remember the exact date) he was expelled from France and entered Spain, where the authorities had been already informed by the french police. So he was detained in Madrid after some weeks and sent to Cadiz in order to put him in a boat to La Habana even some weeks latter. It's also a funny passage the way he tells it. Another thing he tells is that at the time he didn't speak spanish, but he started to study it during his staying at Cadiz. Certainly in Mexico in 1940 he spoke it.
That's the point, the only place he wanted to go in the Americas was New York. So, even if he doesn't manage to avoid the travel to La Habana, he would try to enter the USA from Cuba ASAP. But yes, the Cuban authorities could expell him to Mexico, why not, though probably, I guess, their first option would be the USA (it's closer).
I agree with the rest, some minor influence in some leftist enlighted sectors is possible. Again, in this scenario, once the Russian Revolution starts he would leave Mexico for Russia.