You guys are right. The more I've looked into this and considered the situation, the majority of the members of the Confederate government wouldn't go for this plan, as it WOULD be seen as defeatism.
HOWEVER....in the wake of Lincoln's death, and the rise to power of the Radicals who would want to seek revenge upon the South, I believe a few of the more moderates in the government and or the aristocracy at large WOULD start to worry more about their own skins and not about "the Cause". With this in mind, I see these few individuals setting up settlements in Cuba. They would tell the others later on, as the war started to turn for the worst and their idea of having somewhere to flee is vindicated. And as the war begins to end, more and more would try to flee, though not all would make it thanks to the Northern Blockade. Those who do make it to Cuba would begin to rebuild. AFTER the war is over, and the blockade eases up, many Southerners would likely try to flee the persecution of the invading Yankees.
As far as the Spanish in Cuba...the Confederates would make arrangements before hand. Swear nominal allegiance to Spain in return for limited autonomy in their own lands. They'd pay taxes when needed. But they'd also be bribing locals to be more helpful as well.
At least that's how I see this type of scenario playing out.
They might want to flee but the logical place is Mexico not Cuba as ships and boats are expensive and there is NO MONEY! A few Southerners, sure. Enough to matter, no. Even going to Mexico will be difficult as you need supplies on the march and again you have no money.