AHC/WI: Batista's Invasion of Francoist Spain

https://en.wikipedia.org/wiki/Cuba_during_World_War_II#Bru_and_Batista

According to the end of the second paragraph of this section of the Wikipedia page, at one point Fulgencio Batista suggested to the US to launch a joint US-Latin American invasion of Francoist Spain. It never happened, though, probably because the US was busy in the Pacific and other parts of Europe to open another front on a neutral country.

But is it even possible for this to happen, and what would happen if it did? If the US, Cuba, and whatever Latin American nations are in the war (maybe Mexico and Brazil) decide to plan an invasion of Spain, I don't think Britain will support it initially, as it will definetly lead to Spain joining the Axis, which likely means that Gibraltar is going to be overrun. Although, this might lead to Portugal also joining the war on the side of the Allies (could be for multiple reasons, for example, the session of Galicia and/or Spanish colonies, the Anglo-Portuguese Treaty, and so on).
 
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