I'm extremely interested about this topic. I've conducted my own research but wasn't able to find answers specifically to this. It would be very helpful if this were to be answered.
Sorry, what's the actual question you want answered?
Speaking specifically to the issue of Cuba, the impact of the war on the island was minimal. I'd be happy to recommend some authors (all in Spanish, sorry) on the subject to get some kind of info on what happened, but no major military campaigns happened in Cuba during Queen Anne's War (AKA War of the Spanish Succession). This is as opposed to the French-Indian War (AKA Seven Years War) in which the English successfully captured Havana.
The war had important significance for Cuba later in that the new dynasty implemented major reforms in Spanish colonial policy, but the war itself seems to have left the island relatively unscathed.
Most of my books don't even go into any real detail on the impact of this war. The author who seems to pay the most attention to it is the 19th century Spanish historian, Jacobo de la Pezuela, who due to having lost Peru to Bolivar's forces in the 1820s was obsessed with domestic politics and military issues that Cuba faced during its history. From the 30 or so pages he dedicates to the period you're asking about it seems that the war, as always, impacted Cuban trade and there were some issues with privateers, but that nothing major seems to have happened militarily. There were issues with colonial administrations being unsure who they should be loyal to, but that's about it.
You're free to read Jacobo de la Pezuela's book on Google Books. This is volume 2, which has the pertinent section on Queen Anne's War. Keep in mind, this is a Spanish historian writing in the 19th century in an attempt to teach his colleagues in the Spanish colonial administration how to keep Cuba loyal as well as praise Cubans for being loyal to the crown.